iMac won't boot up

Try running Apple Diagnostics (formerly known as Apple Hardware Test) to help identify any hardware issues with your Mac.

First, unplug all external devices except for the keyboard, mouse, monitor, Ethernet connection (if you're using one), and power supply. Make sure your Mac is turned off. Then turn on your Mac and immediately press and hold the D key. Keep holding it until you see a language selection screen or Apple Diagnostics starts loading. Choose your language and wait for the diagnostics to finish. After it's done, Apple Diagnostics will provide information about any issues found and suggest possible solutions.

Safe Mode startup instructions: Safe Mode

Startup key combinations - Apple Support

However your HD may be dead, if it won't startup all they way then your PRAM battery also may be dead. Your best bet to get your data is to remove the HD from the computer and then send the computer in for recycling to Apple, there is no charge for that service.

Try booting it multiple times. I had a similar situation with an eMac that hadn't been used in years. It took 5 or 6 restarts just to get it to boot. Even then, things weren't quite right, but I was able to copy off what I wanted to recover before I wiped the drive.

You might also keep it plugged in overnight on the chance the PRAM battery is dead (it probably is) before trying the restarts.