It's now up to you how you want to fix this problem. I needed my ESX working so I removed the fuse with soldering tweezers and replaced the fuse with a wire.

If you want to replace the fuse, the current through this fuse is roughly 530mA. I have aquired this value by hooking up the ESX to a current measurement device and let the ESX run for 2 hours with maximum processing and loudness.

The fuse is an "SMD"-Type. The housing is 1206 or 1210.