Why can't my HDTV support a higher resolution for my PC?

I just got my new PC today, its a HP Pavilion A6750F and it uses ATI Radeon HD 3200 Graphics card and I have 22 inch SENS LCD HDTV with a built-in DVD player that comes with HDMI and a PC input. Before ordering my PC, I planned on using this TV as a moniter for my new computer seeing how it worked wonderfully with my old one. I connected the TV to the PC using a DVI connection, it was running smooth at first but than the resolution was very low so than I decided to raise the reso, after that my TV would go black non stop. I thought it was because of my DVI cable so today I went to Radioshack to buy a DVI to HDMI wire for 59 dollars (I think I got ripped), so I hooked it up when I came back, once I booted up my PC, everything seemed really huge and fuzzy/blurry (HD? Yeah right..), I tried changing the resolution, refresh rate, settings and in the end I ended up with 1280 x 720 with 60hz, which is lower than I expected. If I try anything higher, my TV would just lose signal. This is what it says on my TV box:

Specifications

- Panel Resolution: 1680 x 1050

- Aspect Ratio: 16:10

- Contrast Ratio: 700:!

- Response Time: 8 MS

- Power Rating: 120v 60hz



What I don't get is, I used this TV as monitor for my older computer which had weaker specs than my new HP pc, yet it ran everything nicely. I'm losing sleep because of this, someone please help me out here. Thanks in advance!

-Why can't my HDTV support a higher resolution for my PC?
9ordoes the pc have hdmi or dvi or vga? if it has hdmi conect it thru hdmi and set the res on the pc to 1920x1080(1080p) or 1280x720(720p) thos are the two suported reselutions by hdmi. if its dvi or vga set the res on the tv(shoud be a button to do that while you have the tv on pc input mode) to 1920x1200 or 1680 x 1050 and set the pc's res to the same.Why can't my HDTV support a higher resolution for my PC?
The panels native resolution (1680x1050) and the supported input resolution may be different. Consult the manual for your tv to determine the maximum supported resolution. 1280x720 might be the highest resolution it accepts.
how many bits does you graphics card had? ATI HD3200 is an old model, for me i prefered inno3D coz it gives a much better performance