@RMC64
Your games disks might be old and non-working, but given that you said how filty the A500 was, you should try cleaning the floppy drive out, too. Get one of those head cleaner diskettes and run it throught there a few times. A can of air isn't a bad idea, either. I had some Amiga's in storage for a while and when I tried some disks, many didn't work. I cleaned out the drives and the disks started working again.
About your sound. I say, don't ram the monitor volume to any one extreme. Try putting it in the middle so you know it's not at zero volume. Run some stereo or vcr audio through the monitor to test it. If that doesn't work, you know it's the monitor and not the computer. If it does work, then it's probably the computer.
The Y-splitter audio cable dealy you got with the A500 is for an A501. That thing makes it so you can use a TV with the Amiga, and it only has one audio-in hole so it comes with the splitter so you can connect the A500 stereo audio up to it and everything (video + audio) goes out through one cable to your TV. It's a good way to record your Deluxe Paint animations with a VCR, too. Easy peasy home-movie credits, hehe. :-)