Difficulty starting '95 Lumina

My car is having some strange symptoms. Sometimes when I turn the key, nothing happens. Sometimes, it produces a clicking noise that sounds like it originates within the center of the dash. After turning the ignition key on and off a few times, it will eventually start. After it starts, the radio often makes a loud buzzing noise and the display dims as if it is underpowered. When I am driving and turn on the turning signal, the speedometer needle “jumps” in sync with the blinker. The speedometer also shows my speed as being about 10-15 MPH faster than actual speed (verified by GPS). The speedometer used to be dead on. The battery checks out OK. The starting motor has been replaced. That has made no difference except that, when the car does start, it starts faster. Could it be grounding problem. Faulty computer chip?

have the diode in your alternator. I have seen this a couple times before. Basically your alternator is back feeding and causing some voltage issues for sensors. One of them being your transmission speed sensors causing them to read high. A bad diode could also overcharge your battery, and cause any control units to freak out.