A disappearing browser indicates a programming fault took place somewhere. The blue screen with the white letters (the infamous "blue screen of death") indicates a similar fault took place in a critical system module or driver. It could be a hardware problem if many different things are affected. It may be the case that you have some kind of memory hardware problem that can affect whatever program happens to get located in that part of memory. Overheating components could be a cause of such a problem. Take note how long the computer has been on when these things happen to see if there is any pattern (such as it never happens within teh first 20 minutes).
Be sure your virus and spyware protection is up to date to this very day (a couple months ago isn't enough). Then call Dell and ask if they can provide you with some memory test software or other suggestions to deal figure out if there might be a memory problem.
The free Firefox/Thunderbird browser and email client should work fine with SBC as long as the correct setup is done. Since SBC doesn't support those programs, they can't tell you how to set it up. But if you can get them to tell you some specific data like "which protocol? POP3 or IMAP?" and "what hostname for outgoing SMTP?" and "what hostname for picking up email by POP3/IMAP?" you might be able to set up your own accounts on it. Any local computer geeks in you area might be able to help with this.
