Hi calkin
The one detail that I'm not clear on: the Dell pauses during the boot for between one and fifteen minutes, right? During that time, as far as you can tell, there is no disk activity? And during that time, is the Dell logo on the screen the entire time? That's an important clue.
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Dell logo on-screen during startup pause
If the Dell logo is on the screen the whole time of the pause, it would tend to indicate a problem before Windows loads. On most computers, Windows does not begin to load until the "splash screen" of the "BIOS" disappears. Usually the splash screen is the logo of the manufacturer ... and the BIOS is a set of basic instructions that get your computer ready to load an operating system. A cold startup of the system will include a set of self-tests by the BIOS (often referred to as the POST [Power-On-Self-Test]). These can be brief or extensive, depending on settings in the BIOS, and whether or not the computer has experienced an unexpected crash.
Reset the BIOS to Default Settings
If the Dell logo is displayed the entire time of the startup pause, some setting might be wrong in the BIOS. Resetting the BIOS values to defaults might help. Here are the instructions for that:
1) Reboot the computer (or power on the computer if it is turned off).
2) When the Dell logo appears, start tapping the F2 key to enter Setup.
3) On the System Setup screen, press the Right Arrow key to move to the Exit menu.
4) Press the Down Arrow key until Load Defaults is highlighted.
5) Press the Enter key on Yes to Load Optimized Defaults
6) Restart the computer.
Run the built-in Dell Diagnostics
Some of the errors in your logs might have been disk related: running the built-in Dell Diagnostics can help check things.
To start the built-in diagnostics:
1) Reboot the computer (or power on the computer if it is turned off).
2) When the Dell logo appears, start tapping the F12 key to see the Boot Menu.
3) Choose Diagnostics.
I recommend running a fairly full set of diagnostics, just to be thorough.
If the diagnostics find a faulty part, it might be covered under warranty. A lot of Dell systems offer on-site service (one year is often included in the base price). If your mother's Inspiron has an extended warranty (longer than one year), the repair will likely be covered by warranty. Dell offers a four year extension for its in-home warranty: if she has that, they'll come pick it up, and deliver it when fixed (or replaced).
If she has the full in-house on-site warranty still in effect, that's a nice advantage -- especially if the diagnostics don't point to anything obvious. Nothing better than being there with the computer when effecting a repair.
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No Dell logo on-screen during startup pause
If the startup pause happens after the Dell logo disappears - I would still like you to try the two steps above: but the possible causes are more various.
Since these possibilities are somewhat lengthy, I'll wait to hear how the results are for the settings reset & diagnostics .
Good luck!