The chime thing is a factory warning that the doors are now set to lock once theyre closed. Nothing to do with the starter. If they arent going on now tho, then yeah you messed something up.
I'd suggest you test each wire you used and see if its connected right. Really if the car is running right now, I don't know why they couldn't set it up to work. You're only really tapping into 5 or 6 wires for a basic starter and if they arent working for the starter, the car shouldn't be running at all, or they arent hooked up right. Again I want to say its the by[ass module....any info on that?