Won't boot up

Well that’s not a good sign, but a repairable one! Either the OS is missing or damaged on the drive or the drive its self is damaged and will need to be replaced.

As Apple produced a very versions of this model you’ll need to figure out which is yours 20” iMac listing

As an example review this guide on how to gain access to the drive iMac Intel 20" EMC 2105 및 2118 하드 드라이브 교체 it will give you the general idea what’s needed. Be careful as this series uses an older version of SATA interface so you will need a drive which supports the older version SATA II (3.0 Gbps) if the drives spec sheet doesn’t list this you’ll need to find another drive.

Now the tricky part! Hopefully you still have the CD’s/DVD’s that came with the system as you’ll need the OS installer disk to re-install the OS and depending on what your system is your options maybe limited as to the highest version you can run on your system.