Netword connectivity lost after power off. Help needed

Here’s my problem:

After doing an update on the server through Putty using “apt-get update” I tried to reboot from Putty without success. I went to Digital Oceans control panel and did a Power Off followed by a Power On using the button. The Power On did not produce any errors. After this I did not have any connectivity neither from website Putty og SFTP. I tried to Power Off and On several times without any luck, so I decided to restore the site from backup.

In the Backups tap, I selected the latest backup, then Restore droplet and waited for the magic to work. Still no luck. Same problem again. I know the server was fully functional at the time the backup was created. This is telling me, that it is properly a connectivity issue, or the backups made by Digital Ocean is not working properly (which is freaking me out). Either option is within Digital Oceans responsibility, I think.

Next step is creating a ticket [#03010237]. I quickly received a standard letter asking me a lot of first line support questions. I answered them all. After waiting several hours, I got another standard letter suggesting me to try a recover. After Power Off I selected the Recover tab, Boot from Recovery ISO, Power On and then opened the console. First the console reported an error, but after several attempts I got in, and selected the Check Filesystem option. The only error reported was this:

cloudimg-rootfs: 578656/6451200 files (0.1% non-contiguous), 2689713/13078779 blocks

What does that mean? Is this the reason why the droplet is not responding? If it is, how do I fix this?

Please help. It is very urgent.