Hey there, mikael_schiffer!
I'm sorry to hear about your issues with the WD Elements external drive and I'm sorry to hear about your data as well.
I'd recommend you to try uninstalling the HDD as a device from Device Manager ( http://technet.microsoft.com/en-us/library/cc725782.aspx
) and see if that will get the drive properly detected when it reinstalls after the reboot.
I'd also strongly recommend you to test the drive's health and SMART status by running the quick and extended tests from the WD's Data LifeGuard Diagnostic tool. Here's a link to it: http://products.wdc.com/support/kb.ashx?id=1CCseu
You could also try using third-party data recovery tools (at your own risk) but I'd first check the heath of the drive. If the data is really important to you, it's best to turn to a professional data recovery company right away. You can find WD's Data Recovery Partners here as well: http://products.wdc.com/support/kb.ashx?id=gI7qBX
Hope it helps. Keep me posted!