Each DVD movie may take about 7 GB, so hopefully your collection is not too big. But, what you can do is use MacTheRipper to rip each DVD, then use VLC to play them (file open-->Video_TS folder of your movie you want). You can use any good video card that has an S-video out to run the video to your TV (unless your TV accepts the DVI signal). For the audio, use either an external firewire or USB audio interface, or use an internal PCI card that has sound out capabilities and run the stereo outs to your TV (if you wanted to do it on the cheap you could just run the signal from your audio out on the back of your Mac to the audio ins of your TV). If you have a surround system, you need an interface or card that can output the 5.1 signal to input into your home theater sound system.
Once it is all hooked up, you go to Displays preferences and either run two monitors seperate or mirror your display with the TV's picture (easier). To run full screen (to keep all controllers and menu bars off the screen), select the Full Screen option in the menus for VLC.
To continue to use your TV as normal, just hook up the S-video to a different input as the cable signal. Use your input button on your remote to scroll through the inputs.
I think it is much easier to simply open a DVD case and pop the DVD in a regular DVD player when I want to watch, but more power to you.