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VMWare Fusion has the same 8 GB limitation.
Most importantly, what major Parallels version is this? 2? 3? 4?
Is there another Domain Controller in the network? How are the network addresses being distributed? DHCP? Is there more than one DHCP server...
The version of PDM6 you installed is most likely not a version compatible with Lion, download the latest PDM6 from the links in my signature.
There are three parts to migrate... 1) The application itself, Parallels Desktop (PDM) 2) The application settings 3) The virtual machine(s)...
For the lack of space uninstalling Parallels was not the best choice, you could've kept it, what you really wanted was to delete your Virtual...
Before changing versions it's advised you shut down the VM, don't suspend it.