Are you using the same credentials when using the console on the core and the credentials you are using when starting it from WinPE? Do the credentials you are using have the Default All Machines Scope?
It sounds almost like when running it from WinPE it is being granted an IP that is occasionally outside the scope of the credentials that you are using.
We had the same Problem (Server2003).
Restarting the "World Wide Web Publishing Service" on the Core Server solved the Problem.
The next morning, the problem had resolved itself. If it comes up again, I'll try restarting the service. Thanks!