Car dying

I have a '93 Buick Regal Custom. Over the past year she has gotten progressively worse with a stalling problem. She's good for about the first 15 minutes of driving but once she gets to a heated operating temperature she just sputters out. I have to let her sit for about 15 minutes and then I can try again, but the only way she stays on is if she is continually revved above 2k rpm. She is not overheating. I don't know if it's as simple as fouled plugs or something worse.

Also, on top of that, last night we drove her around for about 15 or 20 minutes and then pulled into a Speedway momentarily. When we came out and tried to start her we got nothing at all; no starter click, nothing resembling an ignition trying to engage. We got gauge activity, lights, radio, etc., but nothing from the engine. And about a week ago my speedometer and tachometer either wouldn't work or would register at bizarre settings. The battery and alternator are new. It's like she just gave up entirely. **A possible interesting sidenote, my brother-in-law (from where we got the car) installed a remote starter about a year or so before we bought her. We got her in May of '07.

Do I have wiring AND engine issues or are the two related??