How do I unlock my "disk" on MacBook Pro

A mistake on my part, I believe. Review and follow. Note a change in Step 5. Partition is changed to Erase.

Clean Install of El Capitan

1. Restart the computer. Immediately after the chime hold down the Command-Option-R keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the drive (usually, the out-dented entry) from the side list.
5. Click on the Erase tab in Disk Utility's main window. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Reinstall OS X and click on the Continue button.

Replace the disk.

Follow these instructions:

Clean Install of El Capitan

1. Restart the computer. Immediately after the chime hold down the Command-Option-R keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the drive (usually, the out-dented entry) from the side list.
5. Click on the Partition tab in Disk Utility's main window. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Reinstall OS X and click on the Continue button.

You will have to tell me exactly which model you have.

BTW, you keep referring to something called the Base System disk. Usually, that is not an actual disk, but an installer or installer disc that you may find below the display of "real" disks in Disk Utility. Here is an image of the device list in Disk Utility:

Is this anything like yours? Is it at all possible for you to take a screen shot to post so that I might see what you are seeing?

In this photo were you able at that point to click on the Erase button in the Disk Utility toolbar? i cannot tell what is ghosted or not. This is image 4. And, please don't post any images except what I specifically ask for because it's a lot of unnecessary scrolling.

Please change the volume name from OS X Base System to Macintosh HD.

If you are comfortable using the Terminal command line, then give this a try after starting from the Recovery HD.

Select Terminal from the Utilities menu. After the command line is displayed enter the following:

diskutil list

Press RETURN. You should then see a listing of all the physical disks and logical volumes on each. If you have only one drive, then you should see something like this:

/dev/disk3 (external, physical):

#: TYPE NAME SIZE IDENTIFIER

0: GUID_partition_scheme *480.1 GB disk3

1: EFI EFI 209.7 MB disk3s1

2: Apple_HFS macOS Sierra 479.2 GB disk3s2

3: Apple_Boot Recovery HD 650.0 MB disk3s3

On your system with only one drive the heading, /dev/disk3 should read /dev/disk0. If you look on the line that shows "2" under the "#" column, you should find your disk's name. Mine is "macOS Sierra." At the end of that line, above, you will see, "disk3s2." On your system you should see, "disk0s2."

Now, enter this command line:

diskutil unmount force /dev/disk0s2

Press RETURN. If this succeeds (no errors returned) then Quit Terminal. Select Disk Utility from the Utility Menu. Now, see if you can do the steps to reinstall OS X. This time First Aid should work when the disk is already unmounted.

If you are now able to get OS X reinstalled successfully, then be sure to click on the Mount button in Disk Utility's toolbar before quitting.

I wanted you to see what the display might look like. Yours will not look like mine because I have several drives mounted both internally and externally. You have a single drive system, I assume. If you do not see the Recovery HD, but you have booted from it, then you have a CoreStorage managed drive.

Do you have any way to boot the computer from another bootable device? An external drive or bootable flash drive or another Mac computer that you can connect to this one?

OK, I don't know if this will work because it depends on exactly which model you have. It will work if your computer came with Lion or later pre-installed when it was new.

Clean Install of El Capitan or Sierra

1. Restart the computer. Immediately after the chime hold down the Command-Option-R keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the drive (usually, the out-dented entry) from the side list.
5. Click on the Partition tab in Disk Utility's main window. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Reinstall OS X and click on the Continue button.