Sorry to hear of the issues. A few things you can do:
Check the "log" in the dashboard, and click to see the full output. Search the page for "eth" and see if there is anything like "renaming ethX to ethY". If so, this is udev playing tricks and renaming network devices on you, which can be fixed but can be a bit trial and error.
Try a reboot. On some rare occasions we have seen where the settings for an existing volume or image may not get applied the first time. On reboot it sometimes will start working.
If all that fails and still no luck, it is possible to get the data off of it. The process depends on if it is an ephemeral or volume based instance. Here is the basic process, if you need help we can be more specific:
Ephemeral - on the Instances page, click to make a snapshot in the right drop-down menu. When that completes, in the Images menu, make a new volume from that image. Now continue like it was a volume below...
Volume - In Instances, create a new temporary instance so you can attach the volume and view the data. In Volumes, edit attachments for that volume and attach it. It can then be mounted by looking for a /dev/vdb or similar device, mounting it and getting the data.
I hope that helps!