Hi everyone,

The rotary pump of a machine I bought was generating too much pressure (maxed out) and I couldn't adjust it using the bypass valve. So I took it apart and realized that the bypass was clogged by some metal pieces(looked like a broken spring). cleaned it up and reassembled. Now it won't draw water. The motor is spinning fine, and I can push water through using a syringe, however it won't suction water on its own. Any ideas?

Wild guess, something in the bypass valve broke causing it stuck close and pump over pressure. After clearing the debris (the "metal pieces") the bypass valve now stuck open causing total pressure loss. Remedy, fix the bypass valve if it can be fixed. I could be very wrong as I've never even seen a live rotary pump in my life.

Canatto's right.
If it was working (but not adjustable) before, and now it's still running, but not holding the bypass closed (or something in the bypass is missing and allowing full flow) replace the bypass (If you can get the kit) or replace the pump.

Wouldn't the pump still push some water through at a very low pressure even with a broken/stuck open bypass valve? I'm not getting ANY flow at all

If the bypass wide open, unobstructed, the water's just riding around in circles. If there's no restriction to prevent it from just sucking it's outlet water back into the inlet, it's just going to spin the water around. And, since it's already full, it can't draw in more.
If there is some restriction in the bypass valve, if the valve is complete, sliding nicely and the spring is holding it firmly in the seat, AND there's no restriction to the flow leaving the outlet, then yes, the pump will move the water downstream and draw in new water to replace it. If you're familiar with the pump, you may be able to discern whether it's working against a backpressure or not just by the sound of it and the motor.

Got a new pump today. Replaced it, issue persists. I guess the pump can be ruled out?

I had a similar issue with my Reneka. It ended up being the boiler, the pump would flow water out onto a square metal splitter, 1 of them went to the bottom part of the boiler. I manually filled the boiler up, so when I removed this pipe, I expected water to flow out. It didn't. I grabbed a small skilly screw driver, poked the hole and it was covered up by calcification. After that, my Reneka started pumping water in with no issues. You still may have to prime the boiler through (meaning fill it manually). Maybe this is also what is happening to you.