2004 Starting Problem

My 2004 Taurus SE sedan (28,000 miles) will sometimes require at least two or three attempts to start it. This is problem is intermittent and has only begun since cold weather arrived. Once it does start, a noise much like an old adding machine comes from the instrument cluster and the temperature gage and the fuel gage pointers will fluctuate in time with the clicking noise. When it starts, and the clicking noise ceases, the elapsed time and fuel mileage reverts to zero. Otherwise there are no other apparent problems with this car.

Does the clicking rate fluctuate with engine RPMs? The clicking is probably mechanical but the guages seem more like it's an electrical problem.

The clicking stops after about five seconds. It even does this when the engine is not running.