I would seriously get a new mouse. Logitech optical mice are somewhere around $10 or $15. It's not really worth your time trying to figure it out and probably not worth trying to clean that sucker out.
Microsoft probably did NOT make the mouse. They don't make that shit- it gets made for them. I'm not sure what you are asking for but if it's so you know if it's similar to other mice, it more than likely is. You do not need any special software for a mouse like the one you are describing. I imagine her computer is a little old considering the company went belly up a few years ago.
Computers are one of those things you don't want to buy new every year but every 2 or 3 you should get a new one, regardless of whether you keep or toss the old one. When computers get faster, they try to jam more info and power into programs which makes a bigger and faster computer necessary.