My car did the exact same thing, and I kept going with the intermittent starts until it died as well. I just fixed mine about 15 minutes ago, so let me see if I can help. First thing make sure the wires to the starter aren't corroded, if they have any corrosion, get a little bit of sandpaper or a wire brush and clean them off. Second you said you ripped the aftermarket alarm out. Check to see if there was an ignition kill function, thats what my problem was, I believe the ignition wire is blue with a black stripe or vice versa(thats how it was on my s5) make sure the alarm harness is removed and the connection between where the wires were cut is good, I recommend soldering if they have been cut. If there was no ignition kill, ignore just about everything I just said and replace the ignition switch like everyone else said to do.