Cut away the plug and about 6" of cable - throw the plug away and fit a new plug.
I often repair faults on broken vacs and 75% or more are down to a damaged conductor in the cable - from constant tugging over time.
If it's not this then you only waste 10 minutes and the cost of a plug.
Given what you say it very probably is a bad cable.
Good luck...
Henry Kissinger
September 2014
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