What is wrong with my 2003 Clio, sometimes it just wont start?

I have a 2003 Clio 1.4 dynamique. It has a low mileage and is well looked after. However, alongside with the regular changing of the coils (a common fault I am told) she has now decided to only start when she wants. The car appears to want to start but won’t actually kick in.

I have been told this could be a number of things including, alternator, battery, start motor, TDC sensor. If I change all of these then that’s costly and wont guarantee to solve the problem.

I find that it starts better when it has been stood for a while, like overnight or a good hour (basically when it is cold), if I nip to the shops and come back two minutes later it often wont start.

I have already checked the contacts on the battery and they seem ok.

Any ideas, has anyone else had this problem. I need my car for work so having an unreliable one is not good.

Please help me.