There are several methods for working around internal single tube shorts, but what you'd have to do depends on the actual fault. It sounds like pretty much all of them would be beyond what you'd want to perform.
It's also generally possible to swap in a tube from a donor CRT TV (arcade monitors actually use TV tubes). Given that this is a medium res monitor, you may be stuck swapping the yokes over. Not all TV tubes will be suitable for this particular monitor, but it's generally possible to find one that is. This is a fairly straightforward process for someone who knows what they're doing, but again probably not something it sounds like you'd be comfortable with doing yourself.