P0603 means the PCM is losing Keep Alive Memory (KAM) power. This power is always hot from the battery. If you disconnect your batteries or pull the associated fuse you will get a P0603.
P0605 is a PCM Read Only Memory (ROM) failure. Usually comes up when you have a chip installed that does not perform a checksum.
Have you cleared the codes and if so, do they keep coming back? If you have a chip, pull it, clear the codes and see if the 0605 returns. The 0603 might take some more troubleshooting if the batteries are always connected and the KAM fuse is good.
I clear the p0603 all the time , i have not looked at the fuse , if you could tell me were to look , my edge programer keeps showing the 603 and i just got my AE to work and it came up with p0603 and p0605 . But will look into the fuse first, thanks