Machine won't prime; how to diagnose lack of pump suction?

I recently got a Starbucks Barista machine for free from someone who's had it for 15 years. They hadn't used it in several years, and said the last time it was used it had lost some of it's compression.

I'm currently trying and failing to get it primed. I plug the machine in, click the power button, wait for the ready light, then turn the steam knob. The pump activates, and the steam wand let out a small amount of water/steam, but after that nothing comings out. I opened the back panel, and no water is getting suctioned into the tubing.

I've tried a turkey baster and small pipette to force water into the tubing, but it just squirts out. It's bizarre, because if I squeeze the intake tube slightly, it appears as though it's expelling air (small bubbles come out), rather than drawing it into the tube.

I'd like to diagnose the issue with the machine, so I can buy replacement parts and repair it. My first instinct is the pump is malfunctioning, but I don't know how to confirm that (and I've read that the pump rarely is the point of failure).

I'd love any thoughts or input you have on diagnosing the issue!