Why does my ballcock cistern take so long to fill up?

Nosdda is right as concerns the ballvalve so follow his instructions but he forgot to mention the flushing problem,you don't need a new syphon either as recommended by another guy,what has gone is the diaphragm inside the syphon,they're made of heavy duty nylon and about 4ins diameter,you can copy the shape from a fertiliser bag or similar heavyweight type of plastic,you'll find the biggest problem is removing the syphon,if it's a close coupled WC then you'll have to remove the cistern unless it's a splitter type of syphon,to go into it in detail would take too long to explain,and can be fraught with problems,so good luck.