I installed Version 6.0.2 (1398658) and opted to build the VM from my Boot Camp partition. This partition has been running this version of Win7 for years with no issues.
It does not see a network adapter in the virtual machine. The network part of the vmx:
ethernet0.present = "TRUE"
ethernet0.connectionType = "nat" (This has been every possible thing, I think, as I've tried them all.)
ethernet0.startConnected = "TRUE"
ethernet0.wakeOnPcktRcv = "FALSE"
ethernet0.linkStatePropagation.enable = "TRUE"
ethernet0.virtualDev = "e1000"
I have completely uninstalled and re-installed Fusion and the vm. During the installations, both times the vmWare Core Tools stopped happened. Unchecking open your mac files and web links fixed this. But now I'm wondering if this could be related? Perhaps the tools are out of date or something? The vmWare Tools service says it is running.
I'd also like to mention that the 24/7 support is misleading. Call back on Monday. The support site also will not accept my support request. I guess for $69 you don't get much. Appears that Woody is the only real support option. 
Thanks in advance,
Jack