Toilet does not flush. Bowl fills with water and slowly drain. What could be causing this

Clogged drain... do any other toilets or the tub or any sinks have trouble draining?

Ditto.

Or a clogged vent pipe causing suction and siphoning.

Plunge the toilet aggressively (while water is full up in the bowl)...pulling up on the plunger is more important than pushing down on the plunger (pushing down is only to seal the plunger so you can pull up on it).

If that fails to resolve the issue, go out and purchase a CLOSET AUGER tool (see image) and snake the toilet drain...should fix this up for you!

Mark