You could try pumping the system down with a vacuum pump for 30-45 minutes. That will get rid of most of the moisture in the system. Then, with the system still holding vacuum, charge the first can of R-134a. You can do this without the engine running and with the can upside down to charge it quickly as a liquid. After the first can is charged, the system pressure should be high enough that the compressor will come on when you start it up, allowing you to charge the rest. Charge the rest with the can upright - it is slower, but safer that way. I am not sure, but, if your system is like most, there is a low pressure switch that will not allow the compressor to come on when there is insufficient refrigerant (pressure) in the system.