It could be the power supply unit to start with.
If you have a good knowledge in troubleshooting, have experience in electronics servicing, and have a descent DVM, you can open it up and start with the power input area, and see if it is possible to follow it up.
If you were to buy the service manual if available for this level of device, it would probably cost more than a new answering machine.
During the warranty, these machines are usually exchanged rather than servicing. After the warranty, I would be surprised that Panasonic service would take it for an estimate. The cost of the tech would be too great in relation to the value of the unit.
I have seen this answering machine selling for about $45 to $50 or so. The cost for a service estimate could be just under that amount!