You could get a big ferrite rod from a supplier or off EBay, wrap
several dozen antenna windings around it, and then place it next to and
hopefully parallel to the ferrite inside your old radio. Ground one
end of the wire, and string out the other end of your wire as you wish.
Coupling effects should increase your reception. This would be cheap
and noninvasive, and portable too.

If you can open the radio up, you could even place the new wrapped rod
next to the old one (making sure that there is no direct conductive
effect) and try that. If you do this, watch out, though - if too
close, the stronger signal may overload your inexpensive rig.

Otherwise, wrapping insulated wire around your existing ferrite core
and stretching the remainder around your apartment might work just
fine.

BJ