Are there cables in both ports?
Are both ports configured correctly?
Does the routing have both ports as a default route?
(use: netstat -rn)
If the default route uses both ports, and only one has a cable, you're going to get a 50% failure rate.
When pinging from the laptop: Are you pinging using the IP address or a name that DNS has to resolve? If it's the later, are their 2 entries in DNS, one right, one wrong? It is possible for DNS to toggle between multiple IPs for the same name.