I agree with others that it could be marginal power or antenna connection, but given that the radio receives well and works on low power I would also suspect the problem is a failed component internally, possibly a power transistor or internal power supply issue.
Troubleshooting antenna cable:
1) disconnect both ends, do continuity test between core
and shield. It should fail (no connection).
2) connect a lead with test clips between core
and shield at one end, at the other end do continuity test between core and shield. It should pass.
Troubleshooting input voltage:
1) Figure out a way to measure voltage at the input to the radio by exposing the leads. (Probably the best place is at the inline fuse where you connected it to the house power, but you may need to get creative using extra crimp connectors in a Y cable.)
2) measure voltage while receiving
3) measure voltage while transmitting at low power
4) measure voltage while transmitting at high power
You should expect to see a voltage sag under load, but even at step 4, your input voltage should be at least 11.9v If not, add a parallel connection to the house power and see if it works better.
If these things don't find your issue, try replacing the radio. Last time I had a VHF issue I replaced it, sent the original for factory repair then sold it on eBay when it came back. Good luck.