My Time Machine won't back up and files won't open when double clicked.

Question

I'm not sure if these are related, but recently my MacBook Pro has been acting much more sluggish than usual.
To start, I have a 13in MacBook Pro Mid 2012 model with a 2.5 GHz Intel Core i5 processor and 4 GB 1600 MHz DDR3 memory. I've got it new in the summer of 2012, and haven't had any real problems until now. I have a 1TB Hitachi external hard drive with over 600GB left of storage. I'm running Yosemite.
Lately, as in the past few weeks but more noticeably the past few days, I can't open files if I just double click on them from my desktop or from searching them outside of the application. For instance, if I click on a word document on my desktop, it will cause the work icon to bounce for a while, pretending to open, but it never does. If the application is already running, the file just won't open. If I search from the "open" selection within the application, it works fine. This is true for all of my Microsoft Office apps, Photoshop, Preview, iTunes, and everything in between, all of which I had never had a problem with before.
Next, anytime I try to backup my system using Time Machine, it simply shows the "Preparing Backup" status and never starts. I've had the hard drive and used it as a Time Machine since I got the computer, and have had zero problems at all.
I've tried CleanMyMac2, Memory Clean, and I've always kept my Mac very clean and organized, as in no duplicate files, moving my biggest files onto my hard drive, and deleting any of my unnecessary files.  I know I don't have a ton of RAM left, but I'm honestly not completely sure what to do about that, as this model apparently doesn't have RAM updates available.
Think you all can help?
Thanks so much.

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. You must hold down the shift key twice: once when you turn on the computer, and again when you log in.
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.