2005 Toyota Matrix alternator?

Hello thejunkdrawer

'Disconnecting the battery on a running car can cause short in the pcm and destroy it."

Start with checking the battery

A fully charged battery should read about 12.6 volts. If the battery is reading 12.4 volts or less, it is low (discharged) and needs to be recharged.

Battery Voltage and State of Charge:

12.68v.......... 100%
12.45v.......... 75%
12.24v.......... 50%
12.06v.......... 25%
11.89v.......... 0%
When a battery is shorted, or has a dead cell, it can't be charged when the car is running. If the battery is the problem, replace it.
Next, check the battery cables, positive and negative.
Make sure you have a good ground where the negative cable is attached.
If the battery voltage and state of charge is 75% and the cables are good and clean, the problem is in the alternator (the voltage regulator) alternator must be replace to solve the problem