MacBook Pro keeps freezing then shutting off..

Did you do an erase and install of OS X or just what I posted - re-install without erasing? If you did the former and still have the problem, then make an appointment at the Apple Retail Store - Genius Bar and take it in for service. You can also look for an Apple Store - Find a Store - Apple.

If you have NOT tried an Erase and Install, then try it:

Install El Capitan from Scratch

Restart the computer. Immediately after the chime hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:

1. Select Disk Utility from the Utility Menu and click on Continue button.
2. When Disk Utility loads select the volume (indented entry, usually Macintosh HD) from the side list.
3. Click on the Erase icon in Disk Utility's main window. A panel will drop down.
4. Set the Format type to Mac OS Extended (Journaled.)
5. Click on the Apply button, then wait for the Done button to activate and click on it.
6. Quit Disk Utility and return to the Utility Menu.
7. Select Reinstall OS X and click on the Continue button.

Reinstall El Capitan Without Erasing Drive

Please be sure you backed up.

1. Restart the computer. Immediately after the chime hold down the Command and R keys until the Utility Menu appears.
2. Select Disk Utility and click on the Continue button.
3. Select the indented (usually, Macintosh HD) volume entry from the the side list.
4. Click on the First Aid icon in the toolbar. Wait until the Done button activates, then click on it.
5. Quit Disk Utility and return to the Utility Menu.
6. Select Reinstall OS X and click on the Continue button.

Also, see this User Tip: Basic Steps for Upgrading OS X.

Try each of these in order. Test to see if the computer is working properly:

1. Reset the PRAM
2. Reset the System Management Controller (SMC)
3. Start the computer in Safe Mode, then restart normally. This is slower than a standard startup but is normal.
4. Repair the disk by booting the from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. Select the indented (usually, Macintosh HD) volumeentry from the the side list. Click on the First Aid icon in the toolbar. Wait for the Done button to appear then click on it. Quit Disk Utility and returnto the Utility Menu. Restart the computer from the Apple Menu.
5. Reinstall OS X by booting from the Recovery HD using the Command and R keys. When the Utility Menu appears select Reinstall OS X then click on the Continue button.
6. Download and Install the OS X El Capitan 10.11.4 Combo Update if needed.

Make a "Genius" appointment at an Apple Store, or go to another authorized service provider. You may have to leave the machine there for several days.

Back up all data on the internal drive(s) before you hand over your computer to anyone. There are ways to back up a computer that isn't fully functional—ask if you need guidance.

If privacy is a concern, erase the data partition(s) with the option to write zeros* (do this only if you have at least two complete, independent backups, and you know how to restore to an empty drive from any of them.) Don’t erase the recovery partition, if present.

Keeping your confidential data secure during hardware repair

Apple also recommends that you deauthorize a device in the iTunes Store before having it serviced.

*An SSD doesn't need to be zeroed.

Well, I can't think of two more questionable things to use other than anti-malware software. If you restart the computer does it work again provided you don't use either Chrome or Skype? Are you sure you did not install any other third-party programs? Do you have at least 4 GBs of RAM installed? What happens if you try using Chrome only or Skype only? Don't run both concurrently. What version of OS X are you installing? I assume you were able to use Safari in order to download Chrome and Skype? If so did you have any problem with Safari?

If you can, try to download and post an Etrecheck report:

http://www.etresoft.com/etrecheck

Ciao.

As long as the Utility Menu appears it's completely normal.