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The valves in the compressor are bad as you suspect (90% chance of that)...or you are operating your test gauges so that hot gas flows from the the high pressure connection to to the suction pressure
connection... and.. at the same time the system is about 50% low on refrigerant. (10% chance of that.
To this close the hand wheel on the red gauge connected to the high pressure side, if the suction pressure (low side) changes you were testing with the service manifold set to bypass hot gas to the low side.
Let me know about that in particular without any other assumptions.
The reversing valve could be bypassing high pressure gas to the low pressure side due to leaking internal seals or the valve not switching positions completely.
Diagnosing that is a bit more difficult.
With the compressor running for 10 minutes or so, put your hand on the largest copper tube connected to the compressor, then shut the unit down, If you hear a gushing sound and the suction line warms up quickly then either the discharge valves inside the compressor is bad, or the reversing valve is bad.
If the suction line connected to the outside unit gets suddenly warm but the suction line AT the compressor does not get warm then the 4 way valve is bad.
These are complex instructions, read them over a few times, then conduct these tests a few times until all starts making sense to you... we can go from there.