If I understand this correctly, you are saying that the OP should convert his already lossy-encoded video files to another lossy format (mpeg-2) so that he can play them on outdated optical media in his DVD player? Why would you do this? That's like saying that the best way to read a book is to make a photocopy of a photocopy of it.
To the OP: As TuckBodi said, there are some DVD players that will play other file formats, most often DivX. My brother-in-law has one and it is pretty finicky, and yes, the interface is absolutely horrible. It works if you already have one, but I sure wouldn't spend any money buying one of them.
The PS3 sounds like a nice option. A bit pricey, but you get Blu-ray and games out of it.
How close is your computer to your TV? If they are pretty close together, or if you have a laptop, you could use a DVI-to-HDMI cable (or whatever cable you need for your particular setup) for video and either a standard stereo RCA cable to mini-plug or a Toslink with a mini-plug connector on one end for audio. That's what I use to stream Netflix to my TV. Total cost would probably be less than $20, depending on how long your cable run needs to be.