You most likely have misconfigured DNS as jstokes pointed out. That is why the IP address worked but names do not.

If you think it might be settings some instruction is below (read n800 for 770)
(still think flashing a new used tablet is best...at least all the confusion from that point will be your own fault )

- open Control Panel (from side menu)
- tap on "Connectivity"
- tap middle button at the bottom ("Connections")
- select the connection name for your workplace net and tap the "edit" button
- on the first dialog tap the "Next" button, and again on the second dialog
- if the third dialog is for the WEP key, tap "Next" again
- you should be on the final dialog where it says setup is finished, only it's not : tap on the "Advanced parameters" button
- there, in the midlle tab "IP addresses" you can uncheck the "automatically get, etc." checkbox. Then you can fill in the fields for your 770's IP address, subnet mask, router (gateway) and DNS as given to you by your network admin.
- sometimes a proxy is mandatory, you can configure that in the left tab too.
- save your info and try connecting...