Car is an S4 B6 (2004) and we have just changed the ignition switch which hasn't cured the fault

Sympton : When cold (and only the first time in the day) when I turn the key radio,lights etc. all work but the car doesn't start. If I hold the key in the start position for a couple of seconds it soemtimes fires up. Otherwise I have to leave it for a few seconds and try again (sometimes without success so I have to leave then repeat the process until it starts).
Once started there are no issues for the rest of the day, but in the morning I have the dreaded wait again!!!
Any sugestions appreciated?