It does sound like a power problem, but could also be corrupted settings
or a poor electrical connection in the lens mount. It might be something
simple.
I assume you have tried the usual things, but in case not, here's a generic
list (I not an Olympus expert, although a long time ago I disassembled, cleaned,
lubrictaed and adjusted an OM-1):
1. Try removing the rechargable battery, wait 3 minutes, then replace it.
2. Check that the battery terminals in the camera aren't corroded or bent.
3. Try a different lens, if you have one.
4. Try replacing the BNL-1 battery (around $40). When rechargable batteries
wear out, they still indicate fully charged (voltage is good, but as soon as
you apply a load it quickly drops).
5. If that doesn't work, consider trying a factory reset (if it will stay on long enough):
https://seventrumpet.com/how-to-reset-olympus-om-d-e-m10-mirrorless-micro-four-thirds-digital-camera/You didn't mention if it's an EM-1 or an EM-2, or if it's still under warranty.
If so, then Olympus will replace it. If not, your best bet is talking to an
expert on this model who can suggest other things to try.