i have a dell optiplex 380 that displays this message
Remove the network card if it's a separate card and reboot and run the diagnostics. If it is integrated, disable it and if it passes the diagnostics, buy a network adapter that use a usb port for about $10-15.
It is not practical to spend much money fixing such an old computer. Think about replacing it.
Download and run My Dell diagnostics here: http://dell.to/SUPsn5 and let us know what the results are please.
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