Are the batteries rechargeable? The total voltage could be with fully charged cells 4.8 to 6 volts nominal. One could be a bit low if you are running at 10MHz or above and the other is a bit high.

The 4.8 v will be fine if nothing causes to much of a voltage drop. The batteries may seem fine after everything stops due to rebound. Try a voltmeter when it is running to monitor the voltage to see for your self.

Solution might be to have a separate set of batteries for the PIC and another for the motors. Share the zero rail.

If you are not running rechargables then a regulator is recommended for the PIC. Keep the voltage at 5 volts or less here. If you run the PIC at 4 MHZ or so the voltage can be much lower, check the data sheet under electrical characteristics. A low drop out regulator may also be handy. If the batteries are max voltage 4.8 and you run at 4 MHz then you will not need the regulator.

This "science olympiad ", is this something with a secondary school or university ?