Yes you can buy replacement power leads - any electrical store or hobby electronics shop - even Amazon.
The crud you mention may well be causing the electricity to trip but where is it coming from?
A certain type of electronic component - electrolytic capacitor - is prone to leaking and it may well be this inside the set that's causing the contamination you notice so a new power lead may not be the long-term solution.
A new lead will be very cheap - but if the tripping problem persists - and I suspect it will - the source of the leakage will need to be investigated.
Electricity will be flowing through the crud and the circuit breaker that trips will be detecting that - and switching off as a safety measure.
The power lead is not the problem - it's the contamination.
Good luck...
June 2015