Bad Power Supply, sscorbett.
Usually you have enough power to light LED lights, (Like the harddrive activity LED light for add-in cards, that you see on the motherboard), and spin fans, but Not enough power to turn the Processor on.
Dell Support >Dimension 8400 > Service Manualhttp://support.dell.com/support/edocs/systems/dim8400/SM/index.htm
Technical Overview > System Board Componentshttp://support.dell.com/support/edocs/systems/dim8400/SM/techov.htm#wp1052739
harddrive activity light for add-in cards (SCSI LED)
The Dimension 8400 comes with an ATX style of Power Supply, that has a maximum rated Wattage of 250 Watts.
1) ALL of the LED lights combined use less than 1 Watt of power.
2) EACH fan uses 2 to 3 Watts
3) A typical Processor can use 51 to 125 Watts.
Your Power Supply just has enough power to light that LED light.
Weak voltage power rail.
Replace the Power Supply.
[ There are three power rails inside that SMPS.
Switched-Mode Power Supply.
1) The 3.3 Volt power rail
2) The 5 Volt power rail
3) The 12 Volt power rail ]
The ATX form factor for a Power Supply refers to the size, and shape of the case, for one.
Approximately 6 inches Wide, 5.5 inches Long, and 3-1/2 inches Tall.
The ATX power supply case in the Dimension 8400 however, is shorter in length.
It is 4 inches Long. (Depth)
Not an advertisement for the website, nor manufacturer.
Reference for the case size, and power cables needed,http://www.cputopia.com/hp-400w-dell-dimension-8400.html
Scroll down to see the connectors of the various power cables needed.
You may have a Power Supply with these dimensions, and needed power cables, in an unused computer.
Perhaps someone has upgraded to a better computer, and has an unused computer that you can temporarily borrow the Power Supply for a test unit.
Make sure it has at least 250 Watts (Maximum rated wattage), plus,
1) 20-pin ATX main power cable. (Or a 20 + 4-pin ATX main power cable)http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
[ 20 + 4-pin ATX main power cable,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20plus4
2) 4-pin ATX +12 Volt power cablehttp://www.playtool.com/pages/psuconnectors/connectors.html#atx12v4
Plus the various power cables needed for the Harddrive, optical drive/s, and computer case fan/s, if it/they do not connect to the motherboard.