You'll never get a good sound from that because a tape head picks up magnetic pulses from the magentic tape and then sends them down a wire. This kind of signal differs from the type you'll get out of your line out from the PC, which is a much more fluid and fuller signal.
Imagine, if you will, two pipes carrying water, the pipe representing the tape gets spurts of water as a someone chucks buckets of water down it. The pipe representing your PC is fed directly from a mains hose allowing for your pipe to be constantly filled. Now with the two pipes you still have the same collection method at the other end, imagine someone is fuilling up buckets and moving them along. Works fine for the tape, but for the PC you will get overspilt water whilst the buckets are moving. (Had enough of analogies ?!?)
So your music will sound compressed and hollow.
Get a tape adapter whilst you wait for an amp.