Should a fuse blow if both neutral/live pin in a three-point socket test live in a continuity tester?
Be careful! Death is easy to come by in such situations!

You need to say what you are testing with.
 You need to say what you are measuring relative to.

If any equipment works when plugged in the pump is faulty or unsuitable for testing with.
 If nothing works then something is broken.

If P &amp; N are connected correctly and shorted the a fuse or equivalent will blow.

Measuring a floating conductor with a high impedance input meter may show high voltages due to capacitive coupling.

Make a test unit: Mains voltage light bulb with two probes.
 Test PN PE NE 
 If PE and NE light N is connected to P.
 If PE lights and NE doesn't and PN doesn't then P OK but N O/C.

If no light from any = major problems.

If no light as above, connect a long lead to outside ground. If any light from P/N/E to outside ground = problems. 

You need to establish what voltages are genuinely present that can provide power - not just an O/C meter reading. Draw a diagram and show what does and doesn't light  light bulb.Meter alone can fool you if unloaded.