Unable to ping an ip address from one of two systems. Both systems are on the same subnet going through the same default gateway. Both systems are online.

We have been having intermittent connectivity issues to a database server. Some users occasionally fail to connect to the database and after rebooting their systems they may or maynot be able to connect. I have found out that from my office one system can connect to the database and the other one can't. The system which can connect, is able to ping the server's ip address but the other one isn't. Both systems are able to get to all other network locations. They are on the same subnet and are going through the same gateway. I am not sure if this might be related but this network is primarily using WINS server for name resolution, there is no DNS setup at this point.

That would rule out an individual NIC but it doesn't rule out saturating the pipe between the two offices.  And each end of the pipe has a router.  Each of those is suspect as well.  

It looks like qwest handles both ends, they can likely supply you with some graphic reports on traffic or maybe they have a monitoring tool you can use to what the pipe and see if the traffic is heavy during these outages.