New Install of Ubuntu, but all applications crash shortly after loading

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Examining the information you have given us (esp. "Need some guidance on how to debug") this does not appear to be a bug report so we are closing it and converting it to a question in the support tracker. We understand the difficulties you are facing, but it is better to raise problems you are having in the support tracker at https://answers.launchpad.net/ubuntu if you are uncertain if they are bugs.

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If it was a new install; I'd likely firstly validate your install media (using the `check disk for defects` option to ensure you're not wasting time chasing down problems due to bad install & unnoticed squashfs errors). It's likely any problems were detected, but I'd likely do this if you haven't already anyway.

Next I'd try and run programs from terminal, as the GUI tends to not display problems (unless you've looked in logs). I would also watch for output being send to logs, but the type of program you are talking about (you haven't provided much detail) would direct me where I'd look first, it may be `dmesg`, or `journalctl`, or if apps/programs crashed as you indicate, I'd also look in /var/crash/ for crash dumps. Even if you cannot read all of the crash dump, the name of the file, date-time stamp are huge clues, let alone the first part of the dump is actually somewhat readable.

More detail as to what mean by "various applications" may allow more a useful response.

Also may want to test your RAM is healthy and update to the latest BIOS

This is a new install, with new memory and an updated BIOS.

One of my challenges is that I am not seeing my hardware resources independently, and I think they might not be configured correctly. (This is a Dell 490, it still has a CD ROM drive, for example.) Where would I find the check disk option?

Applications attempted include Firefox, Rhythmbox and Minecraft.

New memory doesn't mean anything. Obviously not been in IT for long. RAM can be faulty on arrival.

re: Where would I find the check disk option?

https://help.ubuntu.com/community/Installation/CDIntegrityCheck maybe useful. How your machine boots the install-media can vary; ie. I can boot the same thumb drive and it'll act differently in a UEFI based machine, to an older BIOS based machine. On some the menu is very obvious & you don't need to do anything (the menu appears), on others you see a keyboard-in-rectangle and person-in-circle where you press a key for the menu to appear. Your machine firmware itself controls which is required (ie. it's machine specific).

If I run `rhythmbox` from terminal, I get no errors on screen but see in terminal

-- start example
guiverc@d960-ubu2:~$ rhythmbox
(rhythmbox:19800): Gtk-CRITICAL **: 00:23:51.013: gtk_box_pack: assertion '_gtk_widget_get_parent (child) == NULL' failed
(rhythmbox:19800): Gtk-WARNING **: 00:23:51.017: actionhelper: action app.play-repeat can't be activated due to parameter type mismatch (parameter type NULL, target type b)
(rhythmbox:19800): Gtk-WARNING **: 00:23:51.017: actionhelper: action app.play-shuffle can't be activated due to parameter type mismatch (parameter type NULL, target type b)
(rhythmbox:19800): Rhythmbox-WARNING **: 00:23:51.761: Unable to grab media player keys: GDBus.Error:org.freedesktop.DBus.Error.ServiceUnknown: The name org.gnome.SettingsDaemon.MediaKeys was not provided by any .service files
(rhythmbox-metadata:19816): GStreamer-CRITICAL **: 00:23:54.289: gst_date_time_new: assertion 'year > 0 && year <= 9999' failed
(rhythmbox-metadata:19816): GStreamer-CRITICAL **: 00:23:54.289: gst_mini_object_unref: assertion 'mini_object != NULL' failed
/usr/lib/python3/dist-packages/gi/overrides/GObject.py:502: Warning: ../../../gobject/gsignal.c:2647: instance '0x5571881f7ac0' has no handler with id '13189'
  return func(*args, **kwargs)
/usr/lib/python3/dist-packages/gi/overrides/GObject.py:502: Warning: ../../../gobject/gsignal.c:2647: instance '0x5571881f7ac0' has no handler with id '13188'
  return func(*args, **kwargs)
(rhythmbox:19800): Gtk-WARNING **: 00:24:02.106: Can't set a parent on widget which has a parent
guiverc@d960-ubu2:~$
-- end example

ie. numerous warnings, in what was a flawless on-screen operation (i started "Queen:I want to break free" then exited). These messages can be great clues as to problems, or probably more so in my case, clashes between my GTK+ setup & my Qt based desktop.

My reaction to new memory is how many hours? or days? did you run memtest before you decided you trust it? Likewise an updated BIOS I'd run something awhile to 'test' the box before I trusted it with anything real (though I know people often use [windows] installs as their 'test', but Ubuntu installs far too quickly to be any sort of test).