@paulakreuzer is quite correct regarding the warranty.
Just make sure to remind them of this posting:
Regarding you other problems, I really hope for you, though I am not too optimistic.
If the dust and dirt getting into the phone through cracks really be the cause for those troubles, that dirt/dust does not go away by putting a new cover over it.
You should at least try cleaning your phone when / before using the new cover.
For cleaning the phone, take a look here:
or here:
I am wishing you all the best and keep my fingers crossed!