I am looking for a basic music software package for my PC that will allow me to digitally edit pre-recorded music (to create medley's for instance) AS WELL AS to digitally change the key of instrumental tracks without altering the tempo of the music.
Steinberg's Wavelab will do that, which is what I use for mastering in my studio. It's not cheap, though. You can probably get away with the Wavelab Elements version, which is cheaper than the full version, and still has everything you need.
Sony's Sound Forge will also do it, which I also own. I believe they also have a stripped down cheaper version, but you'll need to check the features list of the cheaper version to see if it does pitch shifting with time correction or not.
Please note, Sound Forge is PC only, while Wavelab has both Mac and PC versions. You didn't say if you were on a Mac, so I'm guessing you are on PC.
Also note, that simple pitch shifting is very easy to do, but then if you don't want to change the tempo, you have to do time compression or expansion after the pitch shift, which is very hard to do and still sound good with complex musical material. Most of these programs will have a feature in the pitch shift dialog that will ask if you want to preserve the duration/tempo or not, which then basically applies the time correction after the pitch shifting. Many of them will also offer several different methods of doing the time correction, some will sound better on certain material than others. Speeding up is not as hard as slowing something down... so, if you are lowering the pitch of the music, you'll have to speed it back up to retain the tempo, and that's fairly easy. Going the other way becomes much more noticeable much quicker. If you're just doing this for Karaoke for fun, then it might not make too much of a difference to you how good it sounds, but keep in mind that going more than a few whole steps either direction is going to make the time correction artifacts fairly noticeable with all but the best algorithms out there, and even with the best ones, you still won't be able to go too far with it. [2012 update... time compression and stretching algorithms have gotten MUCH better since I wrote this article originally. However, things still progressively get worse sounding the further you try to stretch the audio.]
If you search around on the internet, you may find some free audio editing software that will at least let you do the basic editing for the medleys. Finding a decent pitch shifting program with good sounding time compression will be a lot harder without paying for it.