My car wont start unless I disconnect a wire.

If it is in timing mode, It will run, but, probably not very good, no advance. Unplugging connector may put it in timing mode, yes it will run. There are several cutlass, I looked at cutlass supreme v6.

Any applicable trouble codes? You should be able to check those yourself? At the distributor black wire with red tracer is ground. Purple wire with white tracer is rpm signal, goes to ecm. During cranking and timing set, the ignition module controls spark timing. With everything plugged in, above a certain rpm, the ecm puts 5 volts on the tan wire with black tracer. That tells the ignition module to use the signal on the white wire for timing. If the 5 volts is there and nothing on the white wire, it won't run. I hope I didn't confuse you, just trying to explain part of it.