I agree with Merlin on this one. It sounds more like a hardware-related issue than an OS one, so before going further, I'd be sure to stress-test each component to make sure that it's a-ok. The first I would test would be the RAM, without question. It often has the tendency to be the first piece of hardware in a PC to die, and it could also cause strange issues like those that you've experienced.
Download the ISO:
http://www.memtest.org/#downiso
Boot up with it and let the test run through twice. If there are no errors, it's not likely the RAM. Past that, you might want to run a program like IntelBurnTest to stress-test the GPU, and then something else for the GPU, although it's unlikely for that to be the issue. Regardless, hopefully this isn't an issue that can't be easily fixed.
Regarding Linux, I am not sure about the WMP playlists, and it would depend on their format. Are they proprietary do you know, or a standard playlist format like .pls or .m3u? If the latter, then they'll work no problem at all. They'll work only if the playlist file is inside the same folder as the files though, since the paths would be different. As for Digsby, it's not yet available for Linux, and given that I've been waiting for at least half-a-year to see it happen, I'm not sure it will, at least soon. I use Pidgin day in and day out, and as long as you don't need something bloated like the real MSN client, you'll be fine with it.
Must-have applications in Linux? Personally, I rely on these day in and day out:
Amarok - Full-featured audio player, plays basically anything. Requires a little bit of work for great support under Ubuntu, though, but that's still easily taken care of.
Codeine - Media player, but I use this particularly only for DVDs, since it seems to handle them better than anything else out there.
GIMP - Image manipulation tool, like Photoshop, but a bit lighter. Little clunky at first if you are familiar with Photoshop, but in some small regards, GIMP is even better. It just takes a little time to get used to.
k3b - Superb CD/DVD-burning tool. An alternative that I like is Nero Linux, but it costs like $20.
KSnapshot - KDE application, but works under Linux. Allows extremely easy screenshot taking.
MediaCoder - It's a Windows application, but runs through Wine, and runs well. It's for recoding any of your audio/video. For audio conversion though, I'd recommend dBpoweramp which runs great through Wine.
OpenOffice.org 3 - Full-featured office suite. Good alternative for Microsoft Office (MS Office can run also, but it requires you purchase a program from CrossOver Office.)
Pidgin - IM client, supports almost any protocol.
SMPlayer - Fantastic media player, can handle almost anything. Better than VLC in my opinion, especially for HD content.
Vuze - Great BitTorrent client, but requires Java (so a little more RAM is nice to have.)
Wine - Allows the ability to run certain Windows applications, including SOME games.
I included screenshots for some of these as attachments.
If you do any web development, then tools like FileZilla are a no-brainer, although that's available for any platform. For HTML/scripting I use Bluefish, which has it's problems, but works well for what I need it for. If you ever want to know of a certain type of program for Linux that you might need, just ask and I might know what you are looking for. The same thing goes for Linux in general. If you need any support, just post a thread here.
I should also mention, before preparing to install Linux, you'll want to create a partition for its usage. I am not sure how you plan to do things, but if you plan to wipe the entire drive, then you'll want to download a tool like
GParted LiveCD, boot up with it and then wipe the entire drive, and create new partitions. For a joint Windows/Linux hard drive, I recommend creating a primary partition for Windows, making sure to make it the exact size you'll need it, and then create an extended partition after that, which will contain all of your Linux-related partitions.
All you need to do is create that one extended partition though, and a Linux partition inside of it. Then, when you install Ubuntu or whatever distro you choose, it will be easier to understand. I've included a picture of GParted that shows how I did my partition layout. You don't need to worry about all the Linux partitions there... you'd just need one. I'm pretty sure Ubuntu will have no issue in partitioning it the way it wants during the install, as long as you allow it to overtake that entire extended partition. Always install Windows before Linux, because Linux will update the boot-loader properly, whereas Windows will not (not even Windows 7 would give a damn about Linux being there). You CAN install Windows after the fact... but you just need to know how to go into your grub and configure it, and that's a little more advanced.
If you plan to keep your current Windows install and want to install Linux on the same drive, you'll need to resize that main partition to make room for it. You can do that with a million different tools, but GParted LiveCD is the best free solution. BE SURE to back up your stuff first though, in case anything goes wrong (and I've had this happen once in the past, so be careful).