The good news is that this situation with your wiring can be resolved pretty easily at a low cost. First you will need a way to get the incoming coax cable connected to your 3 coax wires plus to your Comcast provided router/modem. Here is a 1-in 4-out coax splitter that will do the job:
http://www.amazon.com/4-Way-Coax-Cable-Splitter-Video/dp/B001X3Q2R8
Then you will need another coax cable to connect from the splitter into the Comcast router/modem.
After you terminate the 3 Cat5e cables, they will be plugged into the back of the Comcast router in your basement. (I am assuming that the router has 4 lan ports, most do).
Next, you need a secondary router capable of transmitting WIFI. Here is a link to a dual band router:
http://accessories.us.dell.com/sna/productdetail.aspx?c=us&l=en&s=&cs=04&sku=A8777846&ST=pla&dgc=ST&cid=298442&lid=5699059&acd=12309152537461010&ven1=A8777846:100955342709:901pdb6671:c&ven2=:
On the back of this router is a Wan port which you will connect via Cat5 cable to one of your upstairs wall sockets. Also there are 4 lan ports which you can use to connect your computer, printer and up to 2 more devices (I use a HDTV TV tuner which takes the signal coming from the cable TV or antenna and connects to my router via ethernet so I can watch and record TV using Windows Media Center on my computer).
If you need to connect more than one device in the other 2 rooms that have Cat5 wall sockets, you will need a switch such as this one:
http://www.bestbuy.com/site/tp-link-5-port-10-100-1000-mbps-gigabit-ethernet-metal-switch-black/2080181.p?id=1219528555732&skuId=2080181
It is similar to the router/wifi transmitter except it does not transmit WIFI.
Yesterday I suggested turning off the WIFI transmitter in the Comcast provided router/modem in the basement. This may or not be necessary in your situation. In my case, I have my main router/modem that AT&T provided which also transmits WIFI. However, the device sits at the far end of my house on the second floor, and the signal is too weak to go all over the house (about 90 feet long). So I had to buy a WIFI range extender and place it in the center of the house. It picks up the signal from the AT&T router and transmits it further. The only problem I have is when I run Wifispeedtest on a smartphone or tablet, it says the signal from the extender is being interfered with from other signals, including the signal from the main AT&T router. I have tried transmitting on different channels, but still an issue. This is not the same situation you will have because you are not using a wifi range extender, but I wanted to point out the issue of having multiple wifi signals in the house may cause problems (or maybe not). My AT&T modem/router is not a dual band wifi transmitter, so that in itself means a weaker wifi signal. That is why I suggested a dual band router for you.
Others may want to suggest alternative equipment, but this should do the trick. Since you will need a bunch of cat5 cables to connect your computers, printers, etc., you can buy some more bulk cable and practice terminating the ends with the crimping tool kit before you terminate the cables running through the walls. It is really not that hard, you just need good eyesight and some patience. You do have to wire them exactly right, there may be instructions with the kit, or you can certainly find them online.
You may wonder why I needed to use a wifi range extender if I have done a bunch of Cat5 wiring in my house. Good question! My Cat5 cabling was done not for computers, but for connecting a headphone distribution amplifier in my control room to remote 6 channel mixers located in the vocal booth, drum booth, and tracking room so that the musicians can do tracking mixes in their headphones while recording. By the time I had put a computer in my wife's home office which is quite far from the AT&T router/modem, I was too lazy to get up in the 3rd floor attic and run more Cat5 cabling, so I went with the wifi range extender. Maybe next winter when it is cooler in the attic I will run some more cable (but I have said that before last winter also).
Let us know how it goes, and Good Luck!