How do I retrieve pictures (or any files) from an old PC that won't boot?

Simplest way to try first
Remove drive from old PC, change jumper on drive to (s) Slave or (CS) Cable Select

Turn of new computer, open computer case, attach drive to middle connector on the gray cable, attach a power source to the drive

(When attaching the gray connector to the drive, there will be a red or blue line on one edge of the cable, that edge with the color needs to be closest to the power input of the drive)

Turn on PC and go into My Computer and see if the drive is seen