Wireless Network Crashing DHCP

PROBLEM:
I recently had a rather odd problem with my network.  When trying to connect to my wireless network my device would either get rejected entirely, or it would connect to the wireless network but never receive an IP address from the routers DHCP server.  This problem only exists with the wireless network, the wired network has no issues at all, even with receiving DHCP addresses.

TROUBLESHOOTING:
To fix the issue I tried two different wireless routers, both have the same issue randomly.

Next I tried using two routers tied together, one running DHCP and wireless, the other running wired.  But the issue still existed.

I discovered that by unplugging one of my computers I was able to resolve the issue which lead me to believe the router was simply getting overloaded.  Splitting the load between the two routers was supposed to be the fix for that.  However, a home router should be able to handle the load of 6 devices just fine. They aren't all streaming, and it was handling 5 devices just fine before.

I started to wonder if it was simply the DHCP server crashing.  Even though I had reserved specific IPs for most of the MAC addresses, it was still work on the routers part handing them out.  So next I tried staticing all the routers and hard wired computers.  But that didn't work either.

BAND-AID FIX:
I was finally able to fix the issue by separating the wireless network from the wired network with the hardware firewall built into the linksys router.  While this did solve the issue it still didn't tell me what had caused the odd issue in the first place.

RESOLUTION:
After more research and not a little luck I discovered that one of my hardwired computers was causing problems for my network because it was having connectivity trouble. The router port and the cable to the computer don't seem to be the issue so I assume the NIC card is going out and re-transmitting so many packets that it was overloading the router.