Old XBOX game playing/saving on 360, but will not come back on after the console is turned off

I just acquired an old copy of Silent Hill 2 for XBOX which is compatible on my XBOX 360 console. Brought it home, played it - all works fine. Saves fine. But when I turn the game off and shut down the console, I can't get back into the game again. I just get a black screen when I select it. I can hear the disc spinning but nothing else happens.

The first two times this happened, I deleted the memory of the game from the hard drive. This worked. The game booted up normally, but of course, I had to start from the beginning again - which is no fun.

Aside from trying to play the game in one sitting (which is not really possible as our XBOX360 is also our Media Centre link), is there a solution to this problem?

 

Here is the confusing question.

Are you trying to play the game on the xbox.

or the xbox 360???

 

I'm playing the game on XBOX 360. It is compatible, the game works, but doesn't want to save in more than one slot. I've never had this problem with a backwards compatible game before.