Could be a loose connection between the PSU power cord fitting and the PSU transformer - which would mean a new PSU.
More likley I would suspect another loose connection on either an expansion card or a loose power connection.
Check all your connections - remove and re-seat them all - data and power. Reseat all your cards (Video, modem, network card, etc.), memory, power, everything. If it's not a permanent part, remove and reseat systematically until you find the culprit.
You could also remove power and data connecitons for all non-essential hardware then reconnect one at a time and test to see if one of those items has an internal problem (non-essential would include, card readers, floppy drives, dvd/cd rom/burners, etc).