I have found many problems that were easily fixed with just the power supply, either buy adjustments or replacement. It very well could be the power supply and should always be checked. I have gone on service calls and found the power outlet was turned on by a light switch. If it is a switching supply it probably needs adjusting. If it is an original it probably needs rebuilding/replacement.
This is such a common problem I put it in my signature. I put the allways in there on purpose. In ham radios I have a cheap meter hooked up to my supply at all times so I can watch spikes, drops, and losses. I would hook a multi meter to the +5 line a watch for changes when you coin up or do whatever is trigger for your problem. If it is not the +5 volt line then check the +12.
If it is not a supply problem then I would look at inter-connectors/cables.