What is happening is the cursor mask processing is corrupted. It's often one of the first signs of hardware failure in the video system but still could be software.
To rule out software you will have to boot from a clean source (install the proper OS onto an external drive, erase your drive and reinstall if you have a great recent backup, or just boot from an install DVD to see if the pointer masking is still mussed up.)
Hardware failure will persist across software installs. It would be worth trying a safe boot - boot with the shift key pressed from the sound until you see the grey apple.
This will let you know it's something you added to (or has failed on) the mac after the OS was first installed. A clean install will fix things but you'll want to watch as you reinstall apps in case it's a conflict and not just something that broke along the way in the software. It's possible but not likely you reintroduced the corruption if it was saved on the time machine backup you restored. Did you notice if the cursor was fixed when you booted to the clean system?
My experience is this is more often caused by faulty hardware - specifically a faulty GPU or faulty VRAM. This non-unibody mac almost certainly has Intel integrated graphics which use part of the RAM as VRAM. You could try isolating your RAM to see if that helps. If you have a good stick of memory, you would install that while removing your potentially faulty RAM from the system. Also - you could catch one bad stick of RAM by first removing the "left" stick and booting. Then remove the right stick and put the "left" stick in the right side. That way you'll detect a single failure of the ram slot or ram sticks by moving things around and testing.
Even though it's irritating, I've seen machines run for stable for years in this state. It's a tiny part of what the GPU does and that machine otherwise was running in a closet and no-one cared most of the time what was on the screen except for when we needed to update or reboot it. You could get a program to make the mouse larger - but that doesn't cure the real issue.
The official service diagnostic (as opposed to AHT - the bundled hardware tests will not find this failure) for your machine will diagnose this failure, but I wouldn't pay much to run that since you can rule out the cheaper fixes by the steps outlined above. Hopefully it's the RAM or the software - both of which are relatively cheap and not too time consuming to fix. I have had good luck seeing this diagnosed for free at the genius bar so if you're close that might be worth a visit for help isolating it as well as getting a repair quote.
Good luck!
If the original drives does work in an external case but not internally than patrix has the right idea.
We know the old drive is good as it works in an external case
We know the SSD does not work at all because it doesn't work externally or in the Mac.
In both of those cases drives are not working internally, one known bad and one known good.
Unfortunately that points to a problem with the MacBook itself. It could be a loose connector (at the drive end or the motherboard end) And by connector I mean data and power, check both, end to end. Look for breaks, bends, crimps (that are not part of cable routing). Look for dirty or obstructed contacts. Blow some canned air into the contacts. Ifixit.com has come really great take apart instructions for just about every recent model of Mac/iPad/iPhone. Follow along with there instructions and pictures and look for differences in what theirs looks like and what yours looks like.
Logic dictates that the problem is inside your MacBook. the problem now is finding out where and then how to fix it.
Best Answer
You need to either insert a Mac OS installer DVD in the optical drive, or a Mac OS installer USB drive in a USB port. You then need to boot from the installer by holding the option key while starting the computer up, then clicking the installer in the list of available devices.