Question : Cannot Ping LAN computer

I am having problems pinging a computer that is on my LAN. This is so far what I have tried/concluded.
 
-Firewall is turned off
-Tracert Hops once to any other PC on my LAN except this one and some others
-The computer cannot accept pings yet is capable of pinging any computer that I can ping on another computer.
-There is no IPSEC installed; using IPV4
-Managed Switches have no rules applied or filtering
-Router is old as dirt but probably not the case because I can ping random IP's and successfully ping 26 PC's out of 56.

So what gives?? Any Ideas??

Answer : Cannot Ping LAN computer

Ok....So I was reading up on HAL's (Hardware Abstraction Layer) and begun to think that possibly the computer is pulling the wrong HAL somehow. We do image the computers using ghost. But all the computers use the same image within their model. So when some work and others don't it's baffling. I decided to re-install Windows but preserve the programs, there-by resetting the HAL. But I started to configure it and accidently blew away the whole OS. So now working with a clean install it wouldn't work.....Configured the firewall exceptions to allow incoming echo requests under the ICMP. Finally able to ping the computer. But I really hope I don't have to have a clean install on every computer not accepting pings.....So do you think I am heading in the right direction with the HAL or am I chasing my tail. I am running out of possibilities......So what's your take.