1998 ZX6R won`t start up - turns over and runs when warm, just won`t start

I`ve just got an old 1998 ZX6R - the bike runs nice when warm without a problem but I can`t get it to start from the ignition button. Battery seems to have plenty of charge and engine trys to turn over - as in you can hear it (in my opinion) attempting to start, but it doesn`t actually fire up! The issue is, the ignition button makes a noise which to mean is trying to turn over the engine (it makes a positive noise not a dead or dull noise) but it doesn`t even try and fire the engine into life.

The only way I could get it to kick into life today was to bump start it in first down a hill! :thumbdown:

I actually drove it around the block a few times, turned the engine off and still it wouldn`t start. When the engine was hot yesterday, it definately started OK.

The bike is new to me and although I`m fairly competent practically, I have limited understanding of bikes!

Any help as to where to start would be appreciated. Like I say, the bike sounds fine one running and yesterday, it started OK after a good 20 minute drive but today nothing without a bump start!!

Help much appreciated.

EDIT: sorry mods, does this need moving to the technical sub-forum.