505090 is correct, that the power supply requirements are indeed a factor with video cards. (Both the amount of power on the 12v rail(s), as well as the power supply's available connectors <molex and/or 6/8 pin PCI-E connectors.)
Further, other questions to consider:
1. Are any expansion boards currently occupying the single PCI-E X1 slot on your MB? (The small slot below the top most of the 4 slots.) Video cards are either 1 or 2 slot cards. If you have hardware in the smallest slot, you will be limited to single slot cards.)
Assumption: No PCI-E connectors (since it is a HP computer), and the power supply is barely adequate for the pc (all OEMs do this). I would figure something in the range of 400w total, with a total +12v output on a single rail of around 15a.
(You should be able to look on the large sticker attached to the power supply to get this information.)
2. It is never a good thing to a buy a video card that is "too powerful" for your current CPU, unless you plan to buy the video card first. (And, then, move the card to a new computer.)
As such, since you didn't mention what cpu you have, I am going to assume you have the best your MB can take, a AMD Athlon 64 X2 4800+ (duel core, runs at 2.5 Ghz).
3. What games do you play?
(Assumption: Everything but the most modern of games, mostly at medium quality settings)
4. What resolution do you play at?
(Assumption: 1680 x 1050 22" widescreen monitor)
Check your Windows display settings for this information. The smaller the total resolution (mulitple the two numbers), the less powerful the graphics card you need.
5. Does your case have room for an ATX power supply replacement? (Meaning, is your computer's power supply "standard sized.")
Assumption: Yes
6. Are you comfortable enough with computers to replace a computer's power supply?
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If the answer to question 6 is no, then I would recommend the following:
ATI Radeon 4670:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814125277
It doesn't require a separate power connector, SHOULD work with the lower power of your power supply, and will adequately match your processor. It offers multiple video output options, is relatively low priced, and is a respectively powerful card for its kind. (In typical use, it is used in people's home theatre pcs. But, it should work well with your pc's era.)
If the answer to question 6 is yes, and you have the budget to buy a new power supply to, then:
CORSAIR CMPSU-450VX
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139003
Radeon HD 5770 1GB
http://www.newegg.com/Product/Product.aspx?Item=N82E16814102858
This combo supports DirectX 11 (versus only 10.1), has 2X the performance in most games over the 4670, and it will also be a good match for your cpu. (However, your cpu will probably be a limiting factor in some games before the video card.)