If your priority at this point is data recovery, using an All-in-One puts you in a really bad situation as these are basically HUGE laptops with external mice and keyboard and are as hard to service, if not harder, than laptops because the latter older models generally have access panels that make removing the hard drives really easy. But with these, you have to remove the back cover and that's really hard to do without breaking anything.
What I would suggest at this point, since booting is not working properly, is using the information below to create boot media on USB stick, booting from that, connecting another USB stick and then using File Manager to save off the files and folders you need to salvage.
If your PC can not boot into Windows, a way around that is to follow the instructions below to create boot media from Macrium Reflect (MR) that can be used to rewrite/repair the boot media on your PC: 1) Download and install Macrium Reflect (MR) from this link: http://www.macrium.com/reflectfree.aspx 2) Use the option to create a boot USB stick or CD
That will create MR bootable media. Then, you can boot your PC into WinPE using that media.
Have patience, as that can take a while to start and bring up the screen.