I recently purchased a used 2006 Honda Civic Si. The AC system is not working as the system does not blow cold air. The clutch on the compressor is not engaging, however the condenser fan is running fine and all the lights for the AC inside the car come on. I got a can of the recharge refrigerant but the guage indicated not to recharge as something else was wrong (needle in the red). I replaced the compressor relay but still no luck. What is the next step in checking what's wrong?
First of all check if the compressor is still good. Engine off and keys in pocket, reach the compressor with your hands and rotate the clutch hub (the front part on the compressor's clutch assembly). Check for uniform resistance across one whole turn. If it seems to "catch" or can't rotate completely, compressor's bad.
If the compressor's good, locate the clutch coil terminals and check for resistance at them. Should read between 3 and 6 Ohms. If not, either the clutch coil is bad or the thermal switch on the compressor's body (check if it has one, basically something with one cable going to the clutch coil and the other to the terminal) is bad and became permanently open. Also, check for voltage on the compressor clutch power connector coming from the harness when engine is on and AC is on. If the clutch coil terminals shows proper resistance and there's no voltage at the connector, you have to look elsewhere than the compressor (refrigerant charge and leaks, pressure switches, wiring etc).
With your gauge indicating in the red, this would indicate a potentially serious problem with your A/C system. With this, I would strongly advise taking this to a certified Motor Vehicle Air Conditioning specialist for diagnosis as additional specialty tools will be required to determine issue accurately. This condition is likely beyond what a home mechanic can solve on their own without the appropriate equipment and knowledge.
The main issue here is you do not have a proper gauge manifold set to determine what the high side is indicating, and we do not have a "reliable" low side reading. Without a proper high and low side measurements anyone would be guessing at what the problem is.
This could be a problem with the Thermal Expansion Valve (TXV) being jammed, or the system was overcharged by someone at some point, likely the previous owner.
IMPORTANT: Willfully "venting" (discharging to the atmosphere) refrigerant is a violation of federal law in the United States and in many other countries. Recovering refrigerant must be done by licensed and certified personnel only.