The Link LED should remain on when connected via hard-wired ethernet. In other words, this is correct behavior.
Are you able to ping the IP address from the unit?
According to the following knowledge base article, the only way to update the firmware in these units is from the web interface:
http://knowledge.digi.com/articles/Knowledge_Base_Article/Digi-One-IA-IAP-Device-Server-Troubleshooting
Have you tried factory resetting the unit to see if communication re-establishes?