If you can hook up the RCA from the ps3 to the tv, it will effectively be the same thing as hooking up HDMI.
The difference isn't too noticeable to me, but I'm more of an audio person.
Try hooking up the RCA and hope it works.
If so, you can always get the HDMI connector in the tv fixed but RCA will work for the time being.
And if not. It's the input system in the tv. That means its useful for what you can use it for, sadly