While my knowledge is limited to US cable companies, I would assume it mostly applies to your country as well. There are a number of misconceptions you have. I will attempt to clear them up.
Wow it is confusing when you say "over the air NTSC" because I suspect that is what my company uses (in combination with QAM perhaps...), but it is not being transmitted "over the air" exactly...
Cable companies only transmit via a QAM signal, through a cable from various junction boxes throughout your neighborhood; all connected to a central hub in a nearby larger town. Cable companies do not broadcast "over the air". ATSC (digital) and NTSC (analog) only refer to over the air transmissions. This means local channels like (in the US) ABC, NBC, CBS all have local broadcast towers which send digital signals over the air for your roof top antenna or TV's rabbit ears antenna to receive.
The thing is, my cable company "switched from analog to digital" transmissions, but you can only receive the "digital" transmissions by renting a set-top box from the company.
All this means is that the cable company stopped rebroadcasting the analog signal and started rebroadcasting the digital signal they receive from your local channels. If your TV has a QAM tuner (most since 2006 do), then you do not require a set top box to view basic cable channels (local channels). If your TV Tuner card has a QAM tuner (and since it still works, I assume it does), then you do not require a "digital" TV Tuner card.
I assumed the set top boxes were converters that allowed analog TVs to receive digital signal, but since most modern LCD TVs have integrated digital tuners and the box is still needed in order to get the "HD" channels, I am guessing the set-top box is more of a gimmick that only "unlocks" some kind of QAM signal that cannot be received without the "digital converter box [set-top box].
Here's where it gets messy, so I'll break it down step by step:
I assumed the set top boxes were converters that allowed analog TVs to receive digital signal
Yes and no. There are two types of "set top boxes"
1) Digital to Analog Converters or DTAs. These are boxes that will allow you to view the newer ATSC (Free, over-the-air digital) signal on a TV that does not have an ATSC tuner. In the US, if you had a TV that only has an NTSC (Free, over-the-air analog) tuner, you could apply to receive a voucher that would cover the cost of purchasing a DTA box. You could take that voucher to any electronics store and turn it in for a DTA converter box. This box would ONLY work with the digital, over-the air, broadcasts coming from your local channels broadcast towers.
It would not work with any cable company's QAM signal.
2) The cable company set top box. This is the box that your cable company provides if:
A) You have a basic cable subscription and you do not have a TV that has a QAM tuner.
B) You have a cable subscription that includes channels like ESPN, HBO, Showtime, MTV, etc...
For A) the box you receive operates the same as the above DTA (probably should be called a QTA or QAM to Analog). This box does nothing but convert whatever QAM channel you're currently tuned to (remember, cable only uses QAM), to an analog signal that your old TV can receive. If you have a basic cable subscription and your TV (or TV Tuner card) has a QAM tuner (most TVs built since 2006 have QAM tuners), then you do not require a set top box from the cable company.
For B) the box you receive is both a tuner and a decryption unit. Cable companies are required to provide your local channels at no cost other than your base subscription fee (plus licensing, taxes, etc). They cannot force you to pay for any device you do not require. In other words, they cannot force you to pay for a set top box if you can get the same channels for free, over the air. In order to do this, cable companies send these local channels "in the clear" or as it's more commonly called, ClearQAM. Essentially, it's an unencrypted version of the QAM signal cable companies use. All other channels (like the ones mentioned above) are encrypted and require a set top box to both decrypt and tune the signal.
...but since most modern LCD TVs have integrated digital tuners and the box is still needed in order to get the "HD" channels, I am guessing the set-top box is more of a gimmick that only "unlocks" some kind of QAM signal that cannot be received without the "digital converter box [set-top box].
Again, the integrated digital tuners are only for over-the-air broadcasts from your local channel broadcast towers. If any of those digital broadcasts are in HD
(digital does not necessarily mean HD), then your TV, assuming it's capable of displaying an HD image, will do so. I do not believe cable companies have any requirement to provide HD channels without additional cost.
A cable company's only requirement is to rebroadcast the non-HD, digital broadcast from your local channels via a non-encrypted (ClearQAM) signal to your TV. Whether or not your cable company provides high definition channels over the ClearQAM signal is entirely up to them. In most cases (mine included), the HD channels from my cable subscription require a set top box (I want them, so I pay for them) or more specifically, in my case, via a cablecard provided from my cable company and Ceton InfiniTV4 TV Tuner card.
My tuner is in fact NTSC so that explains why I cannot see the HD channels on my computer, but it doesnt explain why my HDTV in my living room can't receive the HD channels. I read the user's manual and it said it had an integrated digital TV tuner, so perhaps this integrated tuner is only ATSC capable and not QAM capable?
This last part about the integrated tuner only able to receive an ATSC signal is correct, but it has nothing to do with your cable company. Only the QAM tuner (which your TV does have) will display whatever is unencrypted that's coming from your cable company. As I mentioned above, the HD channels are probably encrypted.
The thing is, in my country most people dont have money for HD TV so my company is somehow transmitting a combination of "analog and digital" signal in a single cable, but the "digital" signal can only be seen on the TV if you pay for a "converter" (set-top box)
Again, it's not analog or digital. It's QAM from the cable company. If you want HD from the cable company, you need a set top box.
So my intention is to be able to watch these "HD" channels (on my computer) without having to pay them to rent this gimmick box that they offer.
Not possible as the HD channels your cable company provides require a set top box (or TV Tuner card that accepts a cablecard from the cable company).
If I get a QAM capable TV-tuner, then in theory, I will be able to achieve this goal right?
No. As we've established, your TV Tuner card is already QAM (or ClearQAM) capable. It will only tune in whatever channels your cable company transmits over ClearQAM (or in the clear/unencrypted). There is no device on the market today that will enable you to view the encrypted channels (to include your HD channels) without leasing a device from your cable company.
I know this is a lot of information, all at once. The main concepts are:
1) ATSC/NTSC are only for over-the-air broadcasts.
2) QAM/ClearQAM (unencrypted QAM) are the only signal sources coming from cable companies.
3) Digital (ATSC)/QAM/ClearQAM do not necessarily mean High Definition.
-Wolf sends
Facebook
Twitter
Instagram