Im asuming your running XP on that old machine, if so...
1. Go to the "system properties" and see if your network card is listed and
doesnt have a exclaimation point, if it does, reinstall the driver for it.
2. If it shows normally without any problems, go to the "control panel" and
double click on the "network connections" icon, then do a right click on your
"local area connection" icon and click on "repair".
3. If all goes well after a few moments and it doesnt tell you any errors, then
proceed to recheck your internet connection. If it still wont connect, then
there might be a problem in the windows registry for the device or you have
a virus or adware/spyware problem that frequently likes to dissrupt your
internet connection.