I have an HP desktop model 400-034 which has been upgraded to 8.1. I connect through a Belkin N600 N+ wireless router to DSL.
When I originally upgraded I experienced issues with internet connectivity and got error messages indicating that I did not have a valid IP address. The other computers in the house did not have the same issues. After troubleshooting the network I could intermittantly connect but would have to restart the computer several times to get it to connect and then I would loose the connection with any period of inactivity. I assumed that I had performed the update incorrectly so I did a restore on the HP and returned it to factory configuration.
I performed all the upgrades and downloaded all the new drivers before doing the upgrade again. I still have the same issues. I have reset the router to factory, upgraded the firmware, and reestablished the LAN. The other computers in the house connect correctly. It appears that the computer sometimes does not pickup the DHCP address, and when it does connect it periodically dumps the ip address even though the lease time is permanent. When this happens I get the connection icon showing with the yellow error symbol. The problems seem to have lessened since the restore but they still occur.