Looks like it wasn't the sliders.
I pulled the caliper off the disc. Then took the pads out. With the parts apart, the sliders themselves seemed to work fine.
When I pushed on the brake pedal, the pressure would wiggle the whole caliper unit hanging on the wire from the suspension, but the piston itself didn't move at all.
I pushed a little harder and pumped the brakes. All the sudden, the brake pedal went down much further, and the piston moved quite a bit.
It came almost all the way out. I pulled it the rest of the way and could see there was surface rust on it. Probably why it wasn't moving. Can I grind off that surface rust real careful and re-use the piston, or do I buy a new one?
It also looks like the piston dust boot is torn and there is some corrosion inside the caliper bore as well.
I think I am going off to the auto parts store to see what they have there, how much it costs, etc.
Any suggestions people? Please let me know! Thanks.