Weird-acting iMac

I have a 2010 2.93 GHz iMac that's been acting really strange.

It started a while ago.

Applications like iTunes and Safari and Firefox would just suddnely shut down.

Nothing would work.

Then the computer would shut down out of the blue.

When I'd restart the computer, everything would work normally for about 2-3 hours, then the same problems would resurface.

Occasionally, before the sudden shutdowns, the screen image would start showing cracks. These are digital cracks, not actual screen cracking.

Like this:




The computer would also take a long time to start up, and I would seesomething I'd never seen before -- this oval/rectangular thing at startup:




When I took it in to my local Mac repair shop, they recommended I get a new hard drive. (The Mac originally came with an Apple-installed 2 TB hard drive.)

So now I have a new hard drive, and the above problems persist -- except for the random shutdowns.

I am on OS 10.6.8 and when I tried to use disk utility with a brand new hard drive, I got this message:



I've also tried fixing it with the install discs to no avail.

I've tried upgrading a newer operating system, including Mavericks (which is allowed with 10.6.8), but something always goes wrong.

It refuses to upgrade.

I am stuck with the operating system as it currently is.

I'm planning to go back to my Mac repair shop, but since they didn't catch this in the first place, I am worried.

I fear there might be something wrong with the computer that can't be fixed.

Yet it worked fine for 3 years.

Any help/insight would be greatly appreciated. Thanks.

 

Thanks, but what are the chances that a brand-new hard drive would immediately have the same problems that my old hard drive had?

I was worried that it might be that. I've also heard that logic boards are hard/impossible to replace.