Welcome to the boards I will take a stab at this Depending on how old the TL is I dont know how much its hurting or helping you If its a collection account I dont think its helping so IMO I would have it deleted if I could. In order to reopen the acct It will have to go to the OC who can decide to do that. So you would have to talk to the OC have them pull it back and convince them to reopen the account. Depending on who it is I don't see it as likely.
If you want to build credit you could start with a secured credit card from either your local CU, BofA, WAMU or National City etc that way you are building positive history while cleaning up your negatives. Target is quite easy to get, Crown Jewelers is another way to go Its a store card that approves you without a credit check and you have to make a purchase and pay a down payment for it to start reporting if you do a search you can find some more details here.
I believe your scores and the number of derogs on your CR will ultimately determine which path is best for you. The above suggestions are what I have based on the limited information I have. I hope this helps