How to troubleshoot: No login GUI after logout or reboot (new install)

[Kynn Jones <kynnjo@gmail.com>]

Hello!

My newly-installed Debian system (wheezy) is working fine for the
most part, except that the login GUI shows up only after I fully shut
down and re-start the system.  Neither running reboot nor running
logout will result in a login GUI; instead, the display just goes dark,
and the system appears to hang indefinitely.

I'd like to learn how to troubleshoot this kind of problem (as opposed
to trying random fixes I scrounge up online until one appears to work).
At the moment, I don't know where to begin, and would be thankful for
some suggestions.

Thanks in advance!

kj

----------------------------------------------------------------------

(tl;dr)

PS: FWIW, here are the only additional, *potentially* relevant
clues I can provide:

  1. a few seconds after running logout, the computer's monitor
  reports that it's entering power-saving mode; (curiously, this
  doesn't seem to happen after I run reboot);

  2. after I run reboot or logout (upon which display goes dark,
  system hangs, etc.), I press the on/off switch on the computer long
  enough for it to go completely silent (shut down?), and then press
  it again to re-start the system, for one or two seconds the computer
  *sounds* as though it is starting up, but then it immediately goes
  completely silent (shuts down?) again.  I must press the on/off
  switch a third time in order for the computer to *really* re-start;
  from this point on, everything works normally;

  3. this machine (a new Dell workstation) came with Windows 7
  pre-installed in its originally sole hard drive (a 500GB 2.5" SATA
  "non-SSD" drive); to this set-up I added a *second* 2.5" internal
  drive (this time a 1TB SSD), and then, I installed Debian (from CD)
  on this newly-added second disk; although my intent was to leave the
  original ("Windows 7") disk untouched, somehow, after I installed
  Debian on the second disk I lost the ability to boot from the
  original Windows 7 disk, even if I set it (via the BIOS config)
  ahead of the "Debian disk" in the boot order; nonetheless, I can
  mount and read the original Windows 7 drive, and AFAICT, its
  contents are still intact.

By itself, the problem of being unable to boot from the Windows 7
drive is far less important, at the moment, then the problem in this
message's subject line.  Therefore, if the two are unrelated (which
would be my uneducated guess), then please dismiss the former problem
(the inability to boot from W7) as a red herring.