Is the battery alkaline on these? If so, I use a weak vinegar solution to remove the corrosion, and follow with a weak baking soda solution to neutralize the acid.
I've been able resurrect smaller devices like Game Gears with this method, along with recapping of course.
And yeah, the screen issue is almost definitely the LCD/inverter caps leaking like mad. Replace those ASAP.
A good rule on old machines like this though - replace every electrolytic capacitor you can find.
I've gotta do my 160 and 190cs both - the 160's already had the screen caps replaced and it did improve image quality overall significantly. There's still a little vertical ghosting, but that's the nature of these passive matrix LCDs.