iMac Snow Leopard Slowed Down

I've had recent problems with my computer lately and had to reformat it twice. But it now it seems slower. It struggles at using more than one program at a time, and struggles to open 2 tabs in safari one after another.

I've restarted the computer several times.
I have 180 gigabytes free space.
It cannot be updated further due to hardware requirements.

I think might have something to do with the commuter processor but I am unsure.

What's wrong with my computer? And how can I fix it

I start looking at the hard drive first with what you are describing.
Especially after a format /reinstall.
It is "extremely" rare for a processor to die.

Have you run "Repair Disk"?
You would do that by booting to your 10.6 disk, head into Disk Utility from there.

Do you have an external drive that you have created a bootable backup on or can install 10.6 onto and try running from the external?

And how much free space does the hard drive have?

My first thought would be to isolate the hard drive as causing the problem. Hard drives can sometimes pass all tests, but just run slow. As you've already reinitialised the hard drive you must have an external drive you've backed up to. If you have space on it, install a fresh Snow Leopard system on it (don't erase it first), add your apps, and copy enough data over for current use. Then boot from the external, and use it to determine if you still have the same problems. If you still have issues, you may have a defective hard drive, or as below.

After previously reinitialising the hard drive, did you use Time Machine to restore to the drive? If so you may have a software problem, and be copying it back to the drive. This is another possibility.