car wont start, lock, unlock, no power

I bought this car not even 2 months ago. The car has been in the shop for over a week but they need to duplicate the problem and of course it did not happen till the last day. He went to turn the car on and it would not start. They replaced the battery and everything was fine and dandy, till it happened yet again same problems. While driving the radio resets and the Toyota logo comes on. It happened again last night while driving home and when I got home I got out of car and tried to lock with no success. I tried manually locking, tried turning the car back on with no success.No symbols pop up so I cant even tie it to a code. I walked away for a couple of seconds several times, after the third time it finally turned on and was able to turn on and off the car and lock.