It's either the charging circuit, the capacitor or the flash tube, but unless your camera is still under the Olympus two year worldwide warranty
(if purchased from an authorised Olympus Dealer within Europe, proof of purchase required) then you'll have to either send the camera to Olympus
for a repair estimate (this costs £15 if you choose to have the camera returned unrepaired) or take it to an independent camera repairer for diagnosis.
The above links/prices are for the UK but should help you navigate to your own country if different.
Alternatively, don't bother with the repair of the pathetically weedy onboard flash and invest the money on a proper external flash instead. You don't have to buy the overpriced Olympus/Panasonic offerings; there are cheaper non-dedicated flash units (you'll need to learn a little bit about how to use them, but they are VERY cheap) or you can buy the excellent Metz 48 AF-1
which is available as an Oly/Panasonic unit and in the UK/Europe is cheaper than a genuine Oly/Panasonic flash. Metz are the undisputed market leaders in flash units and always retain an excellent resale value.
Hope this has helped you, please return the favour by taking a moment to rate my answer.