Since I know asking you to read parts of the owners manual may add confusion.
I am going to borrow some of the text from the Dell 531 owners manual and post it here. Credit goes to Dell computers Inc. for the following content in this post.
Starting the Dell Diagnostics From Your Hard Drive
The Dell Diagnostics is located on a hidden diagnostic utility partition on
your hard drive.
1 Ensure that the computer is connected to an electrical outlet that is
known to be working properly.
2 Turn on (or restart) your computer.
3 When the DELL™ logo appears, press <F12> immediately.
Select Utility Partition from the boot menu and press <Enter>.
NOTE: If you see a message stating that no diagnostics utility partition has
been found, run the Dell Diagnostics from the Drivers and Utilities media.
4 Press any key to start the Dell Diagnostics from the diagnostics utility
partition on your hard drive.
Starting the Dell Diagnostics From the Drivers and Utilities Media
1 Insert the Drivers and Utilities media.
2 Shut down and restart the computer.
When the DELL logo appears, press <F12> immediately.
3 When the boot device list appears, highlight CD/DVD/CD-RW and press
4 Select the Boot from CD-ROM option from the menu that appears and
5 Type 1 to start the CD menu and press <Enter> to proceed.
6 Select Run the 32 Bit Dell Diagnostics from the numbered list. If multiple
versions are listed, select the version appropriate for your computer.
7 When the Dell Diagnostics Main Menu appears, select the test you want
Dell Diagnostics Main Menu
1 After the Dell Diagnostics loads and the Main Menu screen appears, click
the button for the option you want.
NOTE: It is recommended that you select Test System to run a complete test
on your computer.
Test Memory Run the stand-alone memory test
Test System Run System Diagnostics
Exit Exit the Diagnostics
2 After you have selected the Test System option from the main menu, the
following menu appears:
NOTE: It is recommended that you select Extended Test from the menu below
to run a more thorough check of devices in the computer.
Express Test Performs a quick test of devices in the system.
This typically can take 10 to 20 minutes.
Extended Test Performs a thorough check of devices in the system.
This typically can take an hour or more.
Custom Test Use to test a specific device or customize the tests to be run.
Symptom Tree This option allows you to select tests based on a symptom
of the problem you are having. This option lists the most
3 If a problem is encountered during a test, a message appears with an error
code and a description of the problem. Write down the error code and
problem description and see "Getting Help" on page 183.
Also: To enter your BIOS:
Entering System Setup
1 Turn on (or restart) your computer.
2 When the blue DELL™ logo is displayed, you must watch for the F2
prompt to appear.
3 Once this F2 prompt appears, press <F2> immediately.
Please see page 172 of the manual about the BIOS setup utility.
Again here is the link: ftp://ftp.dell.com/Manuals/all-products/esuprt_desktop/esuprt_inspiron_desktop/inspiron-531_owner%27s%20manual_en-us.pdf
I hope I did not over whelm you with information. But if you can get that Dell diagnostic to run, that might help you locate the problem.