My watch is completely dead. Can it be repaired?

Totally dead suggests possibly something as simple as a discharged battery. Check your charging accessories before you admit defeat, and if possible test by substituting at least a known good power adapter, and magnetic cable if you have one available. If that doesn’t get a result Contact Support (link) and arrange to get it checked and diagnosed by Apple Service, they will report your options after examining the watch.

depends on the damage, I would recommend taking it to an apple store and looking at your options.

If it's a dead battery, it can be replaced for $79/plus tax.