SC400 Starting issue

[400Driver]

I've had the car a few years and it recently started having issues with starting. Started when it began to get cold. You can turn the key and nothing happens, no clicks, whirs nada. Wait for a while and it starts fine. Relay? Starter motor? Point me in the right direction. Thanks

 

[400Driver]

Car acts like normal, lights, radio evrything comes on as normal. Turn the key and nothing. replaced battery about a month ago....

 

[400Driver]

Mechanic tells me it's the security system that is faulty on the car. Any work arounds for this?