Was it literally just an upgrade on the PHP side of things and nothing touched within ExpressionEngine itself?
Also just wondering why you can’t upgrade to the latest version? There are loads of good reasons to do so. I’m not sure if 5.3.3 should or shouldn’t work with 1.6.8 so not sure if that’s anything to do with it though. I see from the change log that 1.6.8 was made to be compatible with 5.3.0 but don’t know about other point versions.
Only other thing I can ask is do you have any modules or extensions installed that might be contributing to this at all?
I’ll leave the thread now though and let a moderator come in on this to help you more though.
Hope you get it all working soon.
Best wishes,
Mark
P.S. It might also be helpful to turn on template debugging to see exactly what is going on too.