We're running out of possibilities here.
Using
Safe Mode with Networking gets almost all the software out of the way and begins pointing the finger at a hardware problem. Highly unlikely, though, that both adapters failed at the same time.
Theoretically the Dhcp server on the router could be disabled. Certainly not likely, but please double check using the other computer. If you do an ipconfig /all on that and see "DHCP Enabled. . . . . . . . . . . : Yes" and a good IP configuration you know it's OK. Or, login to the router and actually check it.
If the Recovery included a non-Windows firewall (usually Norton or McAfee) that may be the culprit here; it needs to be configured or uninstalled.