Booster pump for Polaris vacuum not working

[SonicLaw]

When I turn on the booster pump for my Polaris swimming pool vacuum, the pump just buzzes instead of running the motor. I might have a loose electrical wire leading into the switch because the harness seems loose. I'm trying to determine if it is more likely that the booster pump itself has failed and needs rebuilding or replacing.

Thank you for any assistance you can provide.

[PoolDoc]

You may want to check out this Century Motor catalog, and the 2006 AO Smith motor manual:
https://docs.google.com/file/d/0Bxjo2iDF0aJgcnd3WHc1MkJ5b0U/edit?usp=sharing

(I put it on Google Drive, since I can't find it on the Century Electric site.)

Anyhow, the standard B625 is a switchless permanent split capacitor motor according to page 23 of the catalog. The AO Smith motor manual says:

Permanent Split Capacitor. This design does not have a start switch and is often referred to as a “switchless” motor. It uses a run capacitor that remains in the circuit at all times. The PSC design has significantly less starting torque than the capacitor start design
(page 4).

I think that manual covers checking capacitors - you'll probably want to check that out.