99' Galant 157k with Recent Starting Problem Issue

I could really use a professional opinion as to how to proceed with troubleshooting this problem. Have a 1999 Mitsubishi Galant (4 CYL) (157,000 miles) and has been running fine until yesterday. Ran an errand and came out to find the car turning but not starting. Checked the basics before having it towed home. 1. Pulled a spark plug boot and it arced a spark to metal so were good there. 2. Tried spraying starting fluid into air intake (not even a sputter) so I’m guessing it’s not a fuel problem (or maybe starting fluid not making it into cylinder?) 3.I looked through the Oil Cap while my brother tried to start again (Didn’t see any movement) 4. Loosened timing belt cover to inspect belt (same thing its not turning when we try to start) the other accessory belts turn along with the starter but not the timing belt.

Question-Is it supposed to?
I am going to take the cover all the way off now that I’m home and in a garage and inspect the belt closer and see what’s going on.
After removing top timing belt cover i see that the belt is intact, taunt, and no visable damage, I assume inspecting the bottom end is much more involved.
Again, I’m operating on the assumption that the timing belt should be turning and maybe its stripped on the bottom.
What steps should I be taking towards troubleshooting this?
Thanks for your help.