They are the large-ish multi-legged pieces attached to the heatsink and labeled "IC4" and "IC5" on the circuit board. Not sure how you'd check to see if they're burned out apart from just replacing them outright. Maybe someone else can give advice for checking them. Fortunately, they appear to be LM3886, which aren't particularly expensive or hard to find.
What exactly are the symptoms? Is it just not making any sound? Or is it making sound, but it's bad?
So I carried in investigating, swapping the chips over ( with one of them burning out in the process.. oops) to no avail. . I was about to give up, but i thought 'what the heck' and cracked open my other fully working monitor. Connecting this gave me the same result, and hooking my 'broken' amp to the working cabinet reeked in a working monitor. So god knows how, but somehow in fixing the amp I blew both the drivers. Replacements come in above the going eBay rate for a single working monitor, so I'll bide my time, unless anyone here wants to sell their faulty units? (Provided the drivers are good, of course. ..)