That judgement is a kick in the pants. Once you pay it off, find out if you can file a motion to vacate. If you can't file it, ask Discover to file it.
With the CC, you want to let a balance report at statement cut but no more than 9% of your total revolving limit (across all cards).
I would fight tooth-and-nail with the lender of the student loans. Payment history is weighed heavily into your score. See if you can find an executive and email them the info.
On carrying a balance,
Yes, it makes that much of a difference. To FICO, you use your credit, but in a responsible manner.
1) Pay off the judgement, look to have it vacated. I would personally recommend speaking with a contact there, preferably a lawyer who is handling the case. Offer to pay it off entirely now if they will vacate for you. Be nice, not threatening.
2)Contact the federal student loan ombudsman about your lates. Gather all of your facts together first. Be nothing but factual, leave your opinions and slurs and derogatory remarks out.
3) apply for a walmart card now, pay on time.
Do you still have any collections showing on your reports? Even showing as paid in full? Your scores are unusually low based on what you have said. There must be other negative things.