I had to replace my motherboard due to bad capacitors. I just ordered a replacement part from a vendor. It's the same board, part number etc. When I installed the new board, the machine wouldn't power on. I checked cables, connections, but it was just dead.
I then decided to re-install the original motherboard and after I did that, the power wouldn't come on. That too is dead. Any ideas or suggestions?

Dell has built systems with proprietary power supplies and motherboards. If that's the case with yours, installing a generic motherboard might have fried the new motherboard and the power supply.

Sorry, I do not check for private messages

ham30 - read her post again - she said the new mboard is identical.

Assuming you connected the mboards correctly, installed your ram and cpu correctly, etc, your power supply is probably dead.

Dell Dimension 8300

Often you can use a recent or new PS on a brand name computer that originally had a proprietary PS (if it was proprietary - most are not anymore) - I checked that out.
A replacement PS for your computer here:
http://www.power-on.com/atx250dl.html
You can check out the wiring of all the connectors by holding your mouse over them.
In this case, I did that, and the wiring is identical to that for a standard ATX 20 pin power supply.
In this case, connecting a standard PS to the mboard, or the mboard to a standard PS, will work fine, as long as the PS has all the required connectors.

How do you tell if the PS is malfunctioning or dead?
The best way is to borrow a known good PS and try it.
If you can't do that....

If the computer or PS will not start......
Sniff the PS fan outlet area with the power off - a strong burnt wiring / burnt plasticy smell indicates the PS has been overheating or has been malfunctioning, regardless of whether the PS fan is spinning properly.
Try turning the PS fan from the back of the case with a pencil or something slim - it should move in jumps, but be easy to turn - if it is hard to turn, the fan has stopped, the PS has overheated and fried itself, and has died.

If the PS or computer starts up ....
Look in your bios Setup at the current voltages (if you have the monitoring chipset for that) - +3.3, +5, and +12 volts should be within 10% of nominal values - your Vcc (cpu core voltage(s)) should be within 5% of nominal value(s). Voltages that are too high can do a lot of damage in a short time.
If you don't have that in your bios Setup, measure the 12 and 5 volts at the power connectors to a drive - red is +5 volts d.c., yellow is +12 volts d.c., black is negative, probably doesn't matter which one.
The PS fan should be spinning at the speed it is supposed to be - some spin according to how warm the PS is, slower when cooler, but if your PS is as old as your mboard, it may not have that feature and it should spin quite fast. If it spins too slow or has stopped, the PS will overheat and fry itself, malfunction for a while, and eventually die.