As you know, the jag won't power on without a cart in. If the contacts are dirty then it may think no cart is present and not power on.
Alternatively the PSU you have may be problematic.
If the polarity for example was changed by accident from -'ve to +'ve tip (or vice versa i don't remember offhand which is correct) then the Jag wil have waved byebye.
re: the cable...
The edge connector for the Jag is notr a standard size and is a little difficult to find.
Best place to get an AV cable is 1632systems.co.uk or telegames.