How do I get paint off of fiber board?

I have an old shed that was given to me, it has fiber board siding on it. Some of the paint is peeling. I've managed to get that part scraped down. The rest of the paint is like IRON. Short of a match I don't know how to get it off of there. I can't scrap it, I tried sanding it with 100 grit sandpaper, and it won't budge. It won't feather out either
I even tried some of that environmentally friendly stripper. It's supposed to remove up to 5 layers of paint at one time, yeah right. This must be paint it doesn't know about cause it didn't do a thing. I'm afraid if I get too aggressive with the sandpaper grit I'll dig holes with the sander.
There are places where the paint has also checkered. I scraped that until I could see clean fiberboard. (no dirt under the paint) Unfortunately the paint only comes off what was dirty to begin with. It's still checkered only now with wider gaps to fill or do something with.
Is there any kind of product that can be used outside, (like wood filler) that will hold up to NY winter's? Something I could use in the places where the edge won't feather out????

Now I see why it was a gift. I can't afford to put siding on it or I would. Painting it is my only option.

 

I'd just prime and paint it.

You can use exterior spackling to smooth the transision from the scraped/peeled areas to the original finish. be sure to oil prime over it.

 

Thanks
I assume I can get this exterior spackling at Lowes or HD??
Just incase it looks like crap when I prime a small area and the LOML says "DO IT OVER!!" To me is just a shed to store yard tools, in but to her; "people see it ya know!!"

 

I don't know if the big box stores carry exterior spackling or not. A real paint store should have it in stock. Make sure it is for exterior use! Regular spackling won't hold up well outside.

 

I found some at the big box store. It says for interior/exterior. (I have the feeling it won't hold up outside) I also have the feeling that's not what you meant. I'll have to check the yellow pages and see if there is a "real" paint store somewhere close. I know there is one on the other side of the city, but that's 20mi from me. With the cost of gas
I think I'm just going to paint it. If LOML doesn't like it, I'll hand her the scrapper and she can do the other 2 sides of the shed.

 

A couple of coats of primer, sanding between coats should make it less visable. I've used exterior spackling but prefer not to - it becomes the weak link

 

Thanks, that's all I want to hear
I almost always use 2 coats of primer outside, sanding between coats. This will eliminate all the spackling, sanding then prime, then sand again. I'll tell LOML I'll take her out to dinner cause I'll have lots more free time if I don't have to mess around spackling.
I know, you don't need 2 coats of primer, probably a waste, but I find I paint a lot less often than my neighbor