Just trying to recharge with R-134A won't do it.
As Katatac has said you must evacuate before charging.
Here is the procedure to get your A/C working up to spec.
Purge the system of all old refrigerent. Remove the accumulator and the orifice tube. . Now using compressed air blow out all of the old mineral oil from the lines. Some shops flush the lines with solvent but if this gets into the compressor and is not removed it can burnn it out. Now install a new orifice tube (about $3) and put new O rings on all the fittings that you opened, replace the accumulator with a new one (about $30) and put in about 4oz of PAG oil) . Evacuate to 29.5" HG as above, make sure that the system holds vacuum (no leaks) and you are rady to charge. With the engine off put in one car of R-134A with the can upside down (liquid). After this empties, attach another R-134A can to the low side fitting ( this time upright- gas) and start the engine. Put the A/C on max and continue the recharge until proper pressures are obtained. Depending on the temps high side pressures should be 100-200PSI while low side should read about 25-30psi. The temp cycling switch may need to be adjusted ( screw on the cycle switch under connector) a bit to set the cutoff point correctly
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87GT - 3800SC Series III engine, 3.4" Pulley, N* TB, LS1 MAF, Flotech Exhaust Autolite 104's Custom CAI 4T65eHD w. custom axles, HP Tuners VCM Suite.
87GT - 3.4L Turbocharged engine, modified TH125H
" I'M ON THE LOOSE WITHOUT THE JUICE "