As the others said, you need to have a professional evaluate the instrument. I played clarinet for several years in school and I know the abuse a student instrument endures goes beyond dirt and a few sticky pads. If it’s that dirty, there is likely some structural cracking and damage that cleaning isn’t going to fix.
Take it to a shop that rents and repairs student instruments and they should give you a free estimate for what it needs but I would bet what you have is a $35 art piece – hang it on your wall.
You don’t need to throw hundreds into an instrument that will never sound as good as one that was well cared-for. Check e-bay and Overstock. I picked up a brand new student clarinet for $80 online and I’ve seen them even lower priced at Hastings Music and at Costco. You can always upgrade to a higher quality if you become serious about playing, but an entry-level clarinet will get you through student band.