How can I reinstall OS, as my system won't boot up

Sadly, it sounds like your HD is going here given the age of the system.

I would get a new drive but you do have a few issues here:

• You'll need to find a new drive that can run within a SATA I (1.5 Gb/s) system
• You'll need to stay at best Snow Leopard (10.6) if you have the Core Duo system (A1174) or you could go up to Lion (10.7) if you have a Core 2 Duo system (A1207)

Given the age of the system and its limits do you want to spend the money keeping it going or look at a newer iMac that can run El Capitan so your two systems can run the same software without problem? Remember you can't run newer apps on this older system and Apple is not maintaining these older OS's any more so if you're not careful you could get a surprise one day (malware or trojan). There are a used newer systems out there that might be a better investment.

OK, you're going for it! What to do? First I would recommend going with a SSHD drive so you can get some speed improvement (boot up and running apps). The Seagate Desktop SSHD it offers auto sense SATA speed so it will work with your SATA I system. As a reference if we look at the drives spec sheet: Seagate Desktop SSHD specs note the line SATA Transfer Rates Supported (Gb/s) all three data rates are listed SATA I (1.5 Gb/s), SATA II (3.0 Gb/s), SATA III (6.0 Gb/s). Make sure the drive you do get has SATA I listed if not it won't work reliably.

You'll need to follow this IFIXIT guide: iMac Intel 20" EMC 2105 and 2118 Hard Drive Replacement. Makes sure you don't forget to transfer the thermal sensor in Step 22 to your new drive.