You need to take the lid off the cistern and look inside to see if there's any water - no water will make it very hard to flush.
The float valve (ballcock) is to do with controlling the water coming in to the cistern - as the float (ball) rises the incoming water is automtically stopped.
The syphon mechanism manages the flushing - a little harder to fix and if you're not confident with basic plumbing and basic handtools then best left to a specialist.
Sometimes the linkage between the handle and the syphon unit gets itself in a tangle - usually very easy to resolve.
Good luck...
Peccavi
March 2010