Camera won't stay turned on
If you need it you can get the user manual on this link;
The hard reset involves dismantling the camera and un-soldering the memory/clock back-up battery from the main board (check page 112 under batteries). This battery needs replacing after around 3-5 years and is the most likely cause of your problem - they recommend getting it done at an authorised service centre which is good advice unless you have a lot of technical skill - quite a fiddly job to do and to get to - also professional tools are recommended in order not to damage the camera.
Konica Minolta have now passed service responsibility for this camera to Sony - please post back with your location and I can try to find a convenient service centre.
The back-up battery in question is probably relatively cheap (you would have to get the serial number from it for me to check for sure), but the labour involved in replacing it may possibly make the replacement a bit costly, but still should be much less than a new camera of the same quality.
Hope this helps :)