When I read the subject, I initially thought we were going to be discussing a different type of toilet, like those composting styles.  Funny how the mind works sometimes.

Anyway, for your actual problem, I would definitely look at your vent.  The sink doesn't require nearly as much air as the toilet, so it's entirely possible that the sink hooked to the same vent would work ok when the toilet doesn't.  Are you cold enough that you could have frozen your vent pipe?  The ladies room at our church has two stools and one Sunday this winter we had a day with just the right conditions to freeze the vent pipe for those stools and cause them to not flush or flush really slow.  It was quite a problem because we had just been working on remodeling that bathroom and the two toilets had both been replaced that week, so of course we thought something was in the outlet.  A five gallon bucket of hot water carried to the roof and poured down the vent pipe ended up solving the problem.  It wasn't fully frozen (I was the lucky one up there checking it out and pouring the water) but apparently the restriction was enough to cause the problem.

Good luck,

Mike