Yep, that's the fuse and it definitely looks like it's burnt.
This could be all you need to replace to get your system working again. One of the metallic ends should have the fuses' ratings. It should read something like 125V 1.25A (that's what I have in a US TG16), meaning 125 Volts, 1.25 amps.
From what I know, the voltage rating doesn't really matter here but the current rating (amps) is important. Find a replacement fuse with the same amps and you should be good to go.