Yep, the fusebox is melting. When you wiggled the relays, a couple of the wires have touched, creating a "short" to earth.

If you disconnect the battery, then left the base of the fusebox up from its casing @ the back, you should see the problem.

If you pull the back right relay (I believe it is the blue one) which is the main earth system relay for the dim-dip lighting system, then the lights will work normally and this should allow the car to "function" provided it is this section which is "shorting".

This would be a temporary situation though, and I would recommend getting it properly fixed unless you have very good "fire" cover on your insurance policy.