My MacBook is extremely slow

Question

Okay so,
I have a Mid-2012 13" MacBook Pro. I can barely write normally from here, the typing keeps on freezing as many other features in the system (apps, basic tasks, etc)
Specs:
8GB RAM DDR3 1600MHz
1GB Intel HD Graphics 4000
Intel Core i7 @ 2.6GHz
750GB Internal HDD
The macbook was used from 2012 to the last week, it had almost a full hard drive and it was running as slow as ****, but we assumed it was the low HDD space left that was causing it.
Backed it up (we got a 15" new macbook from the year so I use the 13" one now) and started with Command + R, used the Mavericks installation that comes with the macbook and formatted the hard drive and ran a clean install on Mavericks.
Everything went perfect, I created my user and logged in. From the first moment I noticed it was still as slow as before the format, so I waited until indexing was finished. The problem persisted. I get the spinning wheel like every one or two minutes, when browsing it takes a lot of time, sometimes you can't scroll on pages. Everything is just so slow.
Checked the activity monitor, shows a maximum CPU usage with apps running of 25% (75% CPU is idle). The RAM used by programs is about 1.5GB but I generally have less than 4GB free (I know that Mavericks makes use of free RAM because unused RAM is wasted RAM, but to the point of leaving me at 250MB free RAM and the computer running slower than a toaster seems kinda stupid). I'm holding this thing with MemoryClean but it makes no difference.
Tried resetting NVRAM and I think I reset the SMC too, no results.
I am considering bringing it to Apple so they can see what the **** is going on, but I'd like to know if the issue can be solved from home.
Any ideas?
Thanks in advance,
Jose.

Answer 1

Please read this whole message before doing anything.
This procedure is a test, not a solution. Don’t be disappointed when you find that nothing has changed after you complete it.
Step 1
The purpose of this step is to determine whether the problem is localized to your user account.
Enable guest logins* and log in as Guest. Don't use the Safari-only “Guest User” login created by “Find My Mac.”
While logged in as Guest, you won’t have access to any of your documents or settings. Applications will behave as if you were running them for the first time. Don’t be alarmed by this behavior; it’s normal. If you need any passwords or other personal data in order to complete the test, memorize, print, or write them down before you begin.
Test while logged in as Guest. Same problem?
After testing, log out of the guest account and, in your own account, disable it if you wish. Any files you created in the guest account will be deleted automatically when you log out of it.
*Note: If you’ve activated “Find My Mac” or FileVault, then you can’t enable the Guest account. The “Guest User” login created by “Find My Mac” is not the same. Create a new account in which to test, and delete it, including its home folder, after testing.
Step 2
The purpose of this step is to determine whether the problem is caused by third-party system modifications that load automatically at startup or login, by a peripheral device, by a font conflict, or by corruption of the file system or of certain system caches.
Please take this step regardless of the results of Step 1.
Disconnect all wired peripherals except those needed for the test, and remove all aftermarket expansion cards, if applicable. Start up in safe mode and log in to the account with the problem.
Note: If FileVault is enabled in OS X 10.9 or earlier, or if a firmware password is set, or if the startup volume is a software RAID, you can’t do this. Ask for further instructions.
Safe mode is much slower to start up and run than normal, with limited graphics performance, and some things won’t work at all, including sound output and Wi-Fi on certain models. The next normal startup may also be somewhat slow.
The login screen appears even if you usually log in automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
Test while in safe mode. Same problem?
After testing, restart as usual (not in safe mode) and verify that you still have the problem. Post the results of Steps 1 and 2.