My HP Media Centre PC 1280n allows me to record off tv and allows me
to listen to radio.  But there doesn't seem to be any way to record a
song on the radio.  Is this possible.  Is there other
freeware/shareware/cheap software that would allow me to do this and
is easy to use?

Try Windows Media Encoder (see:-
http://www.download.com/3120-20_4-0.html?tag=srch&qt=windows+media+encoder&tg=dl-20&search.x=11&search.y=12
or if the link doesnt work go to download.com and search for windows
media encoder). Thats a freeware program that allows you to (among
other things) capture audio straight from your computers sound card,
so whatever sound can be heard on your computer/through your computers
speakers can be recorded, straight to .wma format (you can find
freeware programs that will convert .wma to .mp3 and other audio
formats, such as I think DBPowerAmp which I use).

Anyway Media Encoder is free and pretty easy to use, I prefer version
7 as the user interface is the simplest :-) it also lets you capture
video if you have a capture card set up and allows you to convert
.avi, .mpg and other video files to .wmv so I find it to be a pretty
useful program!

I hope this helps...