From what I've just read about BCCCode 50, it could be due to problems with faulty hardware or old/bad drivers. Either way, they can cause similar problems.
Since you can boot up, the RAM is probably alright, so my intuition says that it might be bad drivers.
First of all, make sure all your drivers are up-to-date.
Since you upgraded to Windows 7, it might have kept some of your old driver files and that might cause problems.
The wording of your post suggests to me that you haven't manually done anything to update your drivers.
Just to make sure, go to Windows Update. (Type in "update" in the start menu and it should pop up)
Make sure you click the "Check for updates" link and manually select any hardware-related updates.
If you haven't done this, this might fix your problem.
If you manually installed newer drivers for your video or audio, you may have to UNINSTALL them first, THEN re-install.
If the initial install got messed up, it could cause the problems you're talking about.
Additionally, type in "Device Manager" in your start menu, and make note of any devices listed that have an exclamation point or question mark icon on them.
Those are devices that are unknown or are missing drivers, so addressing those may help.
If you need help with that, post the names of the devices with problems, and we'll see what we can do.
If you've already made sure all your drivers are A-OK, and still get BSODs, try uploading copies of those "Files that help describe the problem".
The more specific information we get, the better we can diagnose what the problem is.
In that same vein, if you can figure out some pattern to what you are doing when it crashes, that may help.
Whenever you report a problem, try to provide as much information as you can, paying special attention to the state of the system and what you were doing.
Now, if you really need it up and stable fast, what might help is a repair-install of Windows 7.
To do that, just run the Windows 7 installation disk and follow the directions for repairing and existing install.
If you decide to do this, MAKE SURE IT'S A REPAIR INSTALL. If you do any other kind of install, you may lose your existing files.
Now, you may be wondering, "How did this happen in the first place?"
Well, if you were running Windows 7 fine before you got that downloader, I'd say that you may have had an infection that messed up some of your system files.
If you always had this problem ever since you upgraded, I'd say that if you upgraded from Vista, some old driver files may still be lingering and messing up stuff.
If we eventually determine that it's a hardware problem, you may still be under warranty. But like I said, that possibility seems less probable than it just being driver problems.