HM,
I'm getting confused now -
This statement: "If I power up the laptop and then the wireless PC, I can get both operating together. "
Seems to contradict your earler statment that:
"if the laptop is up and running, the new PC can't pick up a network address when it is switched on."
I would definitely look at how the router is configured to assign IP addresses, handle IP address reservations, MAC address recognition and security.
If they both can recognise the network then the issue is not with the wireless channel in use.
All devices on the same Wireless network will use the same wireless channel. Routers are able to cope with multiple clients, although contention for available bandwidth tends to become an issue far more quickly than with conventional wired Ethernet.
PS - 2 As as in the car (although I have given it to the wife and now drive an Audi, but Baudi Astard didn't have the same ring).