Re: 1998 camaro v6 will not start.
It seems strange the battery will start another vehicle but not your Camaro. The clicking you hear is likely the starter solenoid snapping on and off due to lack of input voltage. Your battery seems weak, but on a good starting engine it is probably good enough, on the Camaro engine where you have to crank it more, it is not up to the job. It probably would crap out on your other vehicle if you had to crank it that long.
Check your battery cables very closely for corrosion, the fact that your added ground wire helped indicates something may be wrong with the factory ground cable. The ground connection must be to the block, and all connections clean and tight. It is very common to see battery cable corrosion on the positive battery cable, even on side terminal batteries. On the inner fender near the battery, there is a power junction block, it should have a power wire in the wiring harness that runs around in front of the battery towards the radiator. Inspect the wires there for shorts or breaks. I had a buddy find bad connections there (in front of battery) that killed his cooling fans & I think caused some starting issues. Once the battery is disconnected the computer loses all learned memory and will be a little bit hard starting & may not idle smoothly instantly, but it should start & run with elevated idle for a few minutes and recover within a few start ups as it re-learns what the engine likes.
Have you tried pouring a small amount of fuel in the throttle body and cranking it? If it tries to start with the added fuel, your fuel pump is probably not working.
Check my web page for First Gen Camaro suspension info: http://www.pozziracing.com
67 RS 327 original owner. 1965 Lola T-70