I would hook the syringe directly up to the cap top tube and pull from there. This will tell you if the cap is sealing correctly and it should pull the ink down through the system fairly easy. Depending on the size of syringe you are using, you should be able to see the ink flow through the damper and head and into the syringe within 2 to 4 pulls. When you pull the syringe, you should be able to see the damper collapse slightly. If you get good pressure and nothing moves through the lines at all, something is clogged and/or the damper could be failing. You could always take the damper off and pull directly on the ink line with the syringe. If ink doesn't comes through that way, something rare is happening such as a clogged needle or ink line.