Possible Computer Problem?

I have a 1996 Chevy Cavalier 2.2 w/5 speed trans with quite a bit wrong. I have various warning lights on that just came on one day leaving work they are ABS, Seat Belt, Airbag, Parking Brake. The car would want to stall if I let the rpms fall to low thus I had to keep them high. I immediately thought low voltage I had my alternator tested and check output voltage while the car was running voltages were normal. I had the starter tested and that was fine because I started to experience a slow starting. Also check battery cables and grounds everything was in excellent condition. I put a new battery in it this past fall voltage good there too. Here is the tricky part and this has happened twice the speedometer stop working and shot up past the max speed and it started fine and I had no lights on all problems were gone. Then the speedometer fixed its self at about 45 -50 mph and problems came flooding back. That has happened twice. This problems just started recently less than a month ago

Any help it greatly appreciated.