Welcome to the forum.
480 is not bad to pay for the belts and water pump replacement if this was in fact done - I'd find a service center that you can trust and ask them to confirm this.
With the engine running check that the alternator is charging and then stop the engine and check that the battery is holding a charge. The charging voltage should be around 13.8 ~ 14.2 Vdc.
Also check the battery terminals and the main connections including to the chassis.
If the car jump starts, then the starter is fine.
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