I don't think I am stealing or ripping off the artist

I have bought plenty of tapes and records in the 80's and 90's. Some of them were lost or didn't survive the test of time. With the digital revolution and the arrival of iPod, I can no longer enjoy them in my car. What is a guy going to do.

If I was to download the songs from limeware, would that be legal because I have already paid the artist and record once before?