Please try each of the steps below that you haven't already taken.
Step 1
From the menu bar, select
▹ System Preferences ▹ Time Machine
and make sure TM is ON.
Step 2
If you're entering Time Machine from the Finder, make sure no Finder windows are open in other Desktop spaces in Mission Control. You must enter from a window open in the current space.
Step 3
If you're backing up to an external hard drive attached to your Mac, open the backup volume in the Finder. You should see a folder with the name "Backups.backupdb". If you instead see a file with a name ending in "sparsebundle," the backup was created over a network. You have to mount the backup volume manually when you want to restore from it by double-clicking the sparsebundle file.
Step 4
Select the "Backups.backupdb" folder and open the Info dialog. Either "staff" or "everyone" should have Read onlyaccess. If not, click the lock icon to unlock the access settings and make the necessary change. If you're not sure how to do that, consult the built-in help or ask.
Step 5
Triple-click anywhere in the line below on this page to select it, then copy the text to the Clipboard (command-C):
~/Library/Preferences/com.apple.finder.plist
In the Finder, select
Go ▹ Go to Folder...
from the menu bar, paste into the box that opens (command-V) and press return.
A folder will open with a file selected. Move the selected file to the Desktop, leaving the folder open for now.
Relaunch the Finder by selecting ▹ Force Quit from the menu bar, then selecting Finder and pressing return. Your Finder settings will be lost.
Try again to enter Time Machine. If you still can't, put back the file you moved to the Desktop, replacing the newer one that will have been created in its place.
Otherwise, close the folder you opened and delete the file you moved to the Desktop. Recreate your Finder preferences.
Step 6
Do as in Step 5, but with this line:
/Library/Preferences/com.apple.TimeMachine.plist
This time you may be prompted for your administrator password. Reboot, recreate your settings in the Time Machine preference pane, and run a backup to test.
Step 7
Launch Disk Utility and select the icon of the backup drive in the pane on the left (not any of the volume icons below it.) At the bottom of the window, you should see this:
Partition Map Scheme : GUID Partition Table
If the partition scheme is anything else, the drive has to be repartitioned (with the loss of all data.)
Step 8
Skip this step if you're backing up to a network device, such as a Time Capsule.
Boot in safe mode. Try again to enter Time Machine.
Note: If FileVault is enabled on some models, or if a firmware password is set, or if the boot volume is a software RAID, you can’t boot in safe mode.
Step 9
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Console in the icon grid.
Click the Clear Display icon in the toolbar. Try again to enter Time Machine. Select any messages that appear in the Console window. Copy them to the Clipboard (command-C). Paste into a reply to this message (command-V).