Bypassing electronic power switch

I Just purchased a computer stereo speaker system from goodwill for $9.00

The power switch is activated by holding down both the up and the down volume buttons. It doesn't work.

I found out after i disassembled the system it has a main circuit board that looks intact. no blown parts visibly.

I checked the bridge diodes and they look functional. One funny thing is if I insert the power plug into the power strip repeatedly it will turn the amplifier on and I can play the amp.

What do I need to know to either fix this problem or by pass the chip that controls the power?

Its a three speaker system two small 3 inch speakers and one six inch speaker for the bass. Its an Altec Lansing ACS45.2

I emailed the company but it has been gobbled up by another company and has no schematic.

Decided to Scrap it for parts.