In theory, HDMI connected cables can transmit the highest quality video most large TV monitors can utilise (1080P - but so will some DVI, and component connections). I expect the 32 inch flatscreen was a TV rather than a very high end exotic monitor of some sort and it's resolution would top out at 1080P.
However, it really all depends on the source files you were going to use, the screen's capability, and the DVD Player =not just the cabling. All of them need to be at least 720P capable for HD Quality. If it's a small file then better hardware won't help. But if it's a decent photo then if the rest of the system is capable, the photos would look superb.
I hope this is helpful.