Id check your BCM, i remember when I did a bit of soldering on it to fix a stereo issue, it triggered my security system to go a bit haywire

 

That's sounds like the starter, the way your describing it sounds like what mine was doing before I replaced the starter then the car was fine.. it could be a short or bad connections though im not sure. As far as security goes I've heard that sometimes when you do work basically anything electrical starter alternator anything like that sometime you have to let the computer reset by leaving key to the on position for about 30 seconds...