Start with the easy stuff !
Your compressor will not engage if there is a low charge in the system. Add a small amout of refridgerate with a die and make sure there are not leaks. Then Get the AC system recharged.
That is the exact same problem that I had on two vehicles, including the Civic. I thought it was a bad compressor as well. Very wrong I was. There was a leak in one of my supply lines, fixed it and got a recharge, then all is good.
I seriously doubt its your compressor.
Last edited by SCoupe; 10-16-2010 at 08:01 PM.