Hello hugofromlondon;
It sounds like your iMac may have had a complete hard drive failure. If it has completely failed, your data may be lost. But, there are still steps you can do to try to retrieve your data.
First, what happens if you try to start your iMac? Do you get the "?" symbol? Was there anything significant that happened before your hard drive stopped working?
1) Have you tried running your iMac from the Recovery Mode? Restart your iMac and hold down the command and R keys, and a spinning globe may appear, then it will ask what language you want to use. After selecting that, you will be presented with a dialog box that has a choice of Disk Utility. Try running Disk Utility and see if it will repair the disk. If it succeeds see if you can restart the iMac to the Desktop. If you can, immediately back up your data to an external device.
2) If Recovery mode fails, you can try putting the problem iMac into Target Disk Mode. With Target Disk Mode you’ll need two Macs, each Mac needs either a Thunderbolt port or a Firewire port. While both Macs are off, connect them with the cable. On the problem Mac hold down the "T" key while it starts up. A Firewire symbol should appear on the screen. Start up the connected Mac and, if everything is successful, your iMac should show up as a hard drive on the attached computer. You should be able to backup your data from that point.
3) Make an appointment with a technician at an Apple Store. They can run some tests to see if your hard drive has failed.
4) There are some third-party companies that make software that may be able to access and retrieve your data. I have not used any recently, so I cannot recommend any.
5) Depending on your experience with the Terminal, if you managed to get into the Recovery Mode, Terminal is accessible from there. Using the command line in Terminal you can look for your hard drive and, if accessible, copy your files to an external drive. This requires some knowledge of basic Unix commands, which can be looked up on the Web.
6) If the data is really important, you can take it to a hard drive recovery company. This is an extremely expensive and time intensive solution, but if the data is highly important, it may be worth it.
Good luck!