Toilet bowl fills and overflows but the tank won't fill
It sounds like there are two problems.  You seem to have a clog in the sewer line slowing the flow of water.  You said it finally drains after a while.  

You also said the tank won't fill.  This sounds like either the flapper is not seating properly, there is a leak between the bowl and tank, or the float has stopped working.

You might need to snake the sewer line if a plunger isn't working.  For the flapper and float, those may need to be replaced.  Mine seem to go out after about 4-5 years.