Try Virtual Machine -> Reinstall Parallels Tools.
Check the settings in Parallels Desktop -> Preferences -> Network -> Shared Networking (click Restore Defaults and make sure Enable DHCP Server is enabled).
Check the Virtual Machine -> Configure -> Hardware -> Network Adapter 1 settings. Try removing the Network Adapter 1 (press [-] button), then adding a new one (press [+] button and select Network Adapter).
Check Windows Start -> Computer -> Manage -> Device Manager -> Network Adapters -> Parallels Ethernet Adapter -> Properties. Does it say "This device is working properly." ? Try right clicking and selecting "Scan for hardware changes".
Open a cmd window in Windows and type "ipconfig" and see if you have an IPv4 address, subnet mask, and gateway.