After you file

Call it $4000 and $5000.  You'd normally get $1000 back.   But the credit would be applied to the other $4000.   

It really depends on the size of the proposed credit ...if the credit is less than $4000 then you don't get it all back...if the credit is greater than $4000, then you get the whole $5k and the excess will get carried over to be (possibly) used the next year(s).

SC ..don't know myself..I would only know if I googled it, and you can do that easier than myself..and it might only apply if you are an actual SC  resident for income tax purposes....not just posted there.  But different states might apply their solar credits differently......and some allow none at all.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*