Dell :: 1080p Output

my finger is currently hovering over the BUY button of a great 1080p monitor at a great price. There is only ONE left in stock and I have a dilema!!! My specs are shown below.

Intel® Core™ 2 Duo Processor T8300 (2.4 GHz, 800 MHz FSB, 3 MB L2 Cache)
4096MB 667MHz Dual Channel DDR2 SDRAM [2x2048]
256MB ATI Mobility RADEON HD 3450
320GB (5.400rpm) SATA Hard Drive
Genuine Windows Vista® Home Premium 64-bit
Fixed Internal 8X DVD+/-RW Slot Load Drive including Software
Primary 9-cell 85 WHr Lithium Ion battery
15.4" Wide Screen WXGA (1280 x 800) Display with TrueLife™

The other day I played a 720p mkv file via HDMI output to a tv, with no problems, picture/sound was fine.

I then tried 1080p output of another video file, via HDMI to the same tv. This tv has a native resolution of 1680 x 1050 and I know that this is not full HD (1080p) which is the resolution of the video I was trying to watch but if I recall the display settings on my laptop were set to 1080p... The video was unwatchable and choppy, pixelated and skipped a lot.

I then tried the same video via VGA with slightly better results, running this time at the natvie resolution of the tv (1680 x 1050). The video was less pixellated but still skipped, enough to make it unwatchable.

I have eliminated the cheap (£3.50!) HDMI cable as the VGA cable was also similar in quality.

My question is this:

Is this poor quality simply due to the fact that my GPU cannot handle pumping out 1080p via hdmi/vga output to a TV? (it plays fine on my laptop's native resolution of 1200x800, although clearly that is not 1080p so it seems that the GPU can handle it?) If the GPU cannot handle it then I am dissapointed as I assumed when purchasing a laptop with a HDMI port that I could output full HD videos to my televsion.

On the other hand if I purchase this new monitor that supports full 1080p HD will the video play ok? In other words, is it the my televison, and not my laptop that is the problem; surely the GPU works just as hard to play the video regardless of what the display output is?