The PSUs in monitors are very similiar to TVs. If you know a good TV repair shop they should be able to repair it for you.
Usually, the smaller establishments with experienced engineers are used to working without model specific manuals. They will likely be able to replace the unmarked cap using their experience to determine a (likely) suitable value.

Edit: Since it's a $600 monitor and since you are here asking these questions I think you should not risk making matters worse by attempting to simply replace the cap yourself. From the sound of things the cap wouldn't have failed so catastrophically in isolation and there are probably other faulty components in the set.
Leave be and get a professional involved, it sounds too nice a monitor to experiment on