The slowness of the computer in general has nothing at all to do with the network issue.
Good news is that is is very simple to change the workgroup back to whatever one it was on before. Just right click on My Computer, choose Properties from the drop down menu, and click on the Computer Name tab. From there just click the change button, and enter whatever workgroup name is needed. You will need to restart the PC.
As for being alow in general, do you have updated AV installed? A firewall? Have you run any type of spyware scans such as Spybot Search and Destroy?