Starting VirtualBox kernel modules ...failed

1) Disable the secure boot on your BIOS settings : Secure boot prevent unsigned modules to be loaded.

2) According to Virtualbox-wiki you need to install dkms module:

Ubuntu/Debian users might want to install the dkms package to ensure that the VirtualBox host kernel modules (vboxdrv, vboxnetflt and vboxnetadp) are properly updated if the linux kernel version changes during the next apt-get upgrade.

Type the following command to install dkms:

sudo apt-get install dkms

Then you can install Virtual-box following the steps described on Virtualbox/Wiki

For Ubuntu 16.04LTS kernel module 4.4.0-22-generic I had to run:

sudo apt-get install virtualbox-dkms.

In my case it was asking to disable secure UEFI. As a side note, the password requested for confirmation needs to be at least 8 characters long.