What should you do if there is a civil suit against you by Capital One for 1088 dollars for a credit card you had in 1999 but you've never received a bill because it was sent to your old address?

Not getting a bill is not an excuse to use in front of a Judge. You still had an obligation to pay and you should have updated your address when you moved. NOw if you got sued and were served at an incorrect address, you can use that as a defense. But all it does is buy you time. If you are liable for the underlying debt, you have to pay. You can argue ignorance of the suit due to a move to negotiate on the acrued interest rate.