Try the pump without any hoses connected.

If it works, work your way toward the nozzles.

There are connections, a check valve, and possibly even a filter.

A check valve looks like a T with a red cap - if you remove the cap, you will find a small spring (do not let it get away!) and a thin disc of flexible material.

I have seen the disc tear, or turn to goop.

You can make a new disc out of a small piece from the cuff of a dishwashing glove - your wife may not even miss it.