Damn man, you just made the whole thing complicated.
In all honesty the TV may display the video, it just may not look right. The refresh rate on a PAL DVDs is lower than NTSC (50 vs 60 Hz) or the other way around. The TV will display SOMETHING (whether it's legible is another problem), it may just look weird. This can range from highly annoying to a mild nuisance. It may also not display at all, depending on the TV. PAL resolution is 625 lines compared to 480 on NTSC, so it's possible you may even be missing some of the picture.
Some DVD players will convert the signal automatically, especially region free DVD players. Go through your DVD player's setup options for video and see if it will do PAL -> NTSC conversion. Should be in the player menus itself (NOT the DVD menus).
Do you have a DVD burner? One option is to get the DVDs, rip them to your PC then convert the video using something like
Nero Vision Express. It's part of the Nero package. You would then have to reburn them to DVD-Rs or DVD+Rs.
The trial lasts for 30 days, so you should be able to squeeze converting them into those 30 days. The cost of the entire package is like $80, so unless you know some
warez else to find Nero, install Nero after you have the DVDs in your possession.
The only other option is to buy a video card capable of outputting to the TV from your PC. Hell, your video card may already have RCA or s-video out. It's a pain in the ass moving it around, but it's an option.
If you give me the model numbers of your TV/DVD/VCR combo thing, I'll check around on the net whether PAL works with your setup or not... assuming I can find anything.