Sorry, I just saw this now. I enjoy wiring. If the purple wire you're talking about is the same one that carguy mentioned, then yes, that would be a problem. If THIS is the case, you might want to do some soul searching, because you can't just cut an unknown wire when you're wiring something up, you need to understand the electrical system pretty well before you start cutting and splicing. My general rule is to not alter or touch factory wiring at all unless absolutely necessary. I leave this to hack alarm installers.
If the purple wire you cut is something different, you still need to figure out what it's for. If restoring the purple wire doesn't fix it, it does sound like it could be a ground to me. Here's what I would do. First, have the battery tested, not just voltage, but a load test, just to rule that out. If that's ok, then I'd check the grounds from the battery to the chassis and the motor. Pay attention to both terminals on the battery too, both where they connect to the battery, and where they connect to the leads. Then I'd check the ground from the motor to the firewall. Next I'd look at the power from the battery to the starter. Next, look at fusible links and fuses. It would be good to have a wiring diagram if it's stock, but you'll need a little more ingenuity if it's been modified. You'll be testing for continuity, and sometimes resistance. A bad connection can show continuity but still have high resistance. Overall, there IS a solution, it may be related to what you did recently, but it could also be completely unrelated and just coincidental. The coincidental ones always irk me, you need to keep an open mind when you're troubleshooting an odd electrical problem, it could be anything. I always just keep it in the back of my mind that, I KNOW there's a problem somewhere that can be fixed, I just have to FIND it. Some good luck is in order as well. 😉