So my MC has been sitting in the garage for some time now waiting to be sold, and it hadn't been started for a while. Silly me should have probably started it every once in a while, because I left the alarm on and a few days ago the battery was dead. No problem, I jumped it and let it run, took it for a spin, all was well. Well a few days later (tonight), I went to start it up again, and it was again dead. But this time I had a much harder time jumping it and something very strange happened. When I would try start it it would not turn over, the solenoid would tick which is OK, but then I heard a strange ticking from the engine bay. I popped the hood and tracked it down to the fuse box. And then tracked it down to the W4 fuse (one of the 4 big ones), labeled by a picture of a fan. I could actually feel the fuse going tick tick tick tick. What the heck is going on?

I eventually got it started and ran it for a while and took it out on a drive. I think it was just jealous of the new MCS, and all now seems well.

But why the ticking fuse?

 

Fuses are very little and thin things - this W4 is probably a relay not a fuse.
What was probably happening was the relay closes a high current circuit (as you suggest maybe a fan) but with a very poor battery, that extra current might be enough th reduce the battery voltage even more and the relay might drop out (especially if controlled from electronics). Then the battery voltage recovers because no more high current, and the cycle repeats.

Get lots of power back in that battery - I've read before it takes up to 20 mins driving to replace the energy lost from starting; if your battery is completely dead (sounds like) you should give a few hours of driving.
Or use a battery charger while it's in the garage ...