ford focus problem, heater always on

Girlfriend's roommate's Ford Focus, maybe a 2000, 2002, something like that.

Even with the ignition off, the power windows and climate controls are operational. If she leaves the heater switched on so she can use the remote start, the blower stays running, killing the battery.

Also, stepping on the brake turns on the brake lights even with the ignition off. Focus brake lights don't normally work with the ignition off.

The cigarette lighter works with the ignition off. I think it's supposed to only work with the key on on this car.

Reverse lights don't work, causing her to fail inspection as well.

All fuses underhood and under the dash test good.

The car has an aftermarket radio, (decently, not greatly) installed with harness. Unplugging it from the car made no difference.

Under the center console, there's a piece of speaker wire not connected to anything. One wire is connected to the parking brake, the other tests as steady ground. It was too cold/dark to take apart the console to see where that other wire is going. I'm thinking maybe the car previously had a DVD player or navigation installed?

There's an Ultra remote start/keyless, and a DEI 556U, which all works properly. They've connected constant, ignition, starter and accessory all correctly. The entire remote start install looks correct, pretty well done, actually. Unplugging the remote starter made no difference.

According to the car's previous owner, this climate-control-always-on problem occured immediately when picking up the car from having the remote starter installed, but they never got around to bringing it back to where it was done.

I saw no other defects or modifications behind the climate control panel, cigarette lighter, or anywhere else.

Any ideas of what I could try next?

Chris, done loads of Foci, never seen this, BUT I did an R/S on an 05 recently where the grey/black starter wire was reading 12volts, even when the plug was pulled from the ignition switch, I took the R/S starter lead out to relay 12 in engine bay fusebox. I would do the following:- Remove all power from the R/S unit, then check, remove power from ignition switch then check, BUT I think Ween is on the money, also reverse light failure is probably at the selector switch if auto (or gearbox) . Could be a failed ignition control relay or bus bar in the fusebox, anyone remember Mkl and ll Golf/Rabbits? Sorry just re-read your post let's face it you've probably done these checks any way.

That is weird, sounds like there's a constant ignition or a constant accessory always powered on.  Do this; disconnect the remote start power connector and check the ignition and accessory wires at the end with a multimeter to see which one is getting fed constant power.  Then you can start to troubleshoot where the problem is.  I think Ween hit the nail on the head.