I think there is a way to connect a portable DVD player to a computer monitor (no computer attachment necessary. I’m not 100% sure that you don’t need the actual computer, but it would be worth looking into it. This way you could just buy the monitor and have a portable player and no TV or computer issues would be involved.
This comment does not negate any of the relevant issues that other posts have and will post regarding watching DVDs at all, just wanted to bring up the issue that possibly neither TV nor computer is necessary to watch a DVD.