Sure, I'll bite.
I follow the belief of both Aquinas and C.S. Lewis, worded so perfectly in the following statement:
[I]His Omnipotence means power to do all that is intrinsically possible, not to do the intrinsically impossible. You may attribute miracles to him, but not nonsense. This is no limit to his power. If you choose to say 'God can give a creature free will and at the same time withhold free will from it,' you have not succeeded in saying anything about God: meaningless combinations of words do not suddenly acquire meaning simply because we prefix to them the two other words 'God can.'... It is no more possible for God than for the weakest of his creatures to carry out both of two mutually exclusive alternatives; not because his power meets an obstacle, but because nonsense remains nonsense even when we talk it about God.[/I]
A boulder that's too heavy to lift or, as Homer Simpson states, "A burrito too large to eat" is not a sign of a lack of omnipotence; it's a matter of being logically unsound. So yes, the argument would still hold that God can indeed be omnipotent and not being capable of logically unsound actions (as one could also argue, at least in the Judeo-Christian system, that God is pure Logic as much as He is Love or Justice).
The second point made in regards to being either fully omnipotent or fully good...or neither... is a case in which I can state with a fair amount of confidence that God is fully [I]both[/I]. It's not a matter of sympathy (despite God having shown that He is one sympathetic to our plight), it's a matter of right and wrong. One can perform a sympathetic act and be doing the wrong thing. Of course, this isn't a blanket statment indicating that God never does sympathetic actions. Far from it! But keep in mind that, yes, God is aware of the actions, reactions, truth and consequences of each act He performs. As we are not, we therefore cannot assume that we know more of the situation than He.
To get to your specific question, though: [i]With all of the suffering in this world why doesn't God do something about it?[/i] Simple. He Can't. Not because He is incapable of doing so; He can erase the entire world should He so choose. No, He cannot because in doing so, we would then introduce His previous gift of [I]free will[/I] and the consequences thereof. You cannot [I]force[/I] someone from performing a good deed. You cannot somehow have a race or a world thrown into sin somehow be 'redeemed' without some price to pay (God's Justice). Fortunately for us, God [I]did[/I] present an unfathomable amount of sympathy toward His creation through the form of the Christ. It was through this one act that we paid nothing and He paid everything. Through this, we are indeed redeemed.
Does this mean the world is now bright and fluffy and oh-so-sparkly clean? No. The consequences of sin are vast and reaching. Something born from sin (imperfection) cannot ever be made sinless (perfect). So we are still within sin's wake. God cannot change that. But what He [I]can[/I] and [I]did[/I] do was provide to us a way to both lift our bearing of it and find a way out.
Nothing short of omnipotence could do that.
Hmm... well, I live on my own so my parents don't have much of a say anymore, now would they? ;) Even when, they were old fashioned enough to just think I still liked watching 'cartoons.' My father was the most vocal about it, but even then it was just an occassional "You're too old for cartoons." I'd shrug and tell him everyone has their inner-kid to appease. Luckily, now I can enjoy anime series at peace, with a fiancee that enjoys it as much as I do. :animesmil