OK, here we go
Regular TVs have a max resolution of 640x480 interlaced.
Interlaced means that to draw a picture it takes 2 passes. The first pass draws the even number lines and the 2 pass draws the odd number lines. It requires these 2 passes to draw a complete picture.
HDTV (16x9) have a max resolution of 1920x1080 interlaced or 1280x 720 progressive, although the vast majority are 1920x1080 interlaced and are not capable of handling 720 p. Front projectors (some, not all) can vastly exceed these limitations
Progressive means the TV draws the complete image in 1 pass.
1080 interlaced requires the same capability as 540 progressive. For example, if 1080 interlaced requires 2 passes, then it draws 540 lines with each pass. 540 progressive draws 540 lines at a time. Therefore a 1080 i TV is also a 540 p TV.
There is also the issue of refresh rate. Refresh rate is the number of times per second the TV draws the picture. For TVs (HDTV or regular), this capability maxes out at 60 cycles/second.
The difference between TVs and computer monitors (or FP) expands both the max resolution and refresh rate limitations. Computer monitors can be driven at much higher resolutions and much higher refresh rates.
IMPORTANT NOTE: DRIVING AN HDTV HIGHER THAN THESE LIMITATIONS (resolution/refresh rate) CAN AND WILL DAMAGE THEM. CAUTION, CAUTION, CAUTION. I would strongly recommend that you stop 'testing' until you understand these issues.
Connections
The next issue is connections. Regular TVs will have video in with RCA jack and maybe s-video in. HDTVs will have component video in (3 jacks) and/or RGB in (standard VGA socket)
In order to get a computer signal into a regular TV, the best bet is to go with something like an ATI all-in-wonder card which has s-video out. I'm not sure if a converter exists to take a VGA signal out of a video card, convert it, and then input it to the TV as s-video.
To get a computer signal into an HDTV requires simply a VGA cable (if the TV has RGD in) or a transcoder which converts the VGA signal (video card) to a component input (HDTV).
I've got to go now, but will continue (expectations and workarounds) when I return.