Interior lights come on randomly, key fob won't open door and won't start

This just happened to me this morning but it occurred two times within about a
four mile span. The interior lights between the front seats came on for about
three or four seconds. It happened again and the only thing I can relate to the
two times is that I was braking the car when it occurred. I've also had a
problem where the doors don't want to unlock with the key fob until I've
pushed the button numerous times. The last thing it does is sometimes it won't
start. I thought it may be a bad battery but I put a load test on it and checked
the voltage, both of those things were good. I hope somebody can give me
some advice.