Usually the only ill effect of magnetized heads is a loss of high frequencies, so the tape is a bit dull sounding. However, this would affect playback for both immediate listening as well as for recording.
If you suspect your tape deck, see if you can borrow another deck from a friend. If that works better you know your deck needs to be serviced or replaced.
And, by the way, 12 years isn't very old for a tape deck. My Nakamichi is about 30 years old and plays fine. The only issue you might run into on a 12 year old tape deck (besides keeping the heads and tape path clean) is the heads may be worn if it has been heavily used. Those aren't too big a deal to have replaced, though you'll likely want a service shop to do it so the alignment of the new head is correct.