Dead Dimension 9200

First, the 9200/410 uses a "BTX" style motherboard, not the common ATX type.  There are very few retail BTX motherboards.

In addition, Dell uses custom OEM motherboards, which are not exactly like a standard "Retail" motherboard.  In many models Dell also uses a proprietary and undocumented front panel connector.  Although possibile to install a non-Dell motherboard with some technical knowledge and possibly some case modification it's best to replace the motherboard with another Dell exact replacement.  In addition, if a non-Dell motherboard is used you will need a new (retail) copy of the Operating System as the Dell will only install on a Dell motherboard.

Try reseating the memory and any PCI/PCIe cards such as a video card and see if that makes any difference.   If the motherboard is bad, there are companies that sell new and refurbished Dell motherboards.  HERE is one vendor I found doing a google search, I know nothing about the vendor - just that I found it on a search.

If you wanted to use a non-Dell motherboard and reuse what components you can from the Dell, the best option is to also buy a new case.  That eliminates the physical installation of a motherboard and also eliminates the non standard Dell front panel connection. 

What you are describing could also be a bad Power Supply or Front IO Panel.  When you try and turn the system does any of the front LED's light up, and if so, which ones?  You could also test out by unplugging the Front IO and seeing if the system light changes to green.