8x8led matrix troubles with 2x 74CH595

TPIC6B595s and TPIC6C595s have been recommended by various people on this board, they are basically the same as the 595 but allow current levels sufficient to drive almost any small LED display. I have them, they work great. I would get a few of those if you have a few bucks to spend. Adafruit sells the B version:

Digikey sells A, B, and C versions. The A allows the highest current and has like 5 pins to ground to support the sinks, B has 3, A has one. All are better choices than a CMOS or TTL 595 which is for logic levels.