Web browsers keep crashing and MacBook Pro keeps restarting

Try setting up another admin user account in System Preferences/Users & Groups to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account 

Safe Mode - About

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply.        Pastebin

Etrecheck – System Information

Use the Snow Leopard DVD or the disks that came with your computer. Do a backup,  preferably 2 separate ones on 2 drives. Boot off the DVD and run Disk Utility Verify/Repair Disk and Repair Permissions until you get no errors.  Reformat the drive using Disk Utility/Erase Mac OS Extended (Journaled), then click the Option button and select GUID. Quit Disk Utility, then re-install the OS.

When you reboot, use Setup Assistant to restore your data.

Update the OS to 10.6.8 and then you can reinstall El Capitan using the link below.

El Capitan

I have the exact same issue for a few months now. I have a late 2008 17" Macbook Pro running El Capitan also. And yes, my web browsers started crashing, and yes, I did create a new profile and it still happened. Sometimes, I can actually get the Macbook to stay on and not crash, so it's sporadic. I notice this started happening after i installed Quicken 2019 for Mac. I believe that messed with my system. I haven't uninstalled it yet, but I probably should. I have not done a clean install yet either. Not sure how to or I would. I want to delete my Parallels and Windows, so I wouldn't mind starting over. Since this system came with Snow Leopard or maybe even Leopard, i don't remember, how do I get it back to El Capitan?

That’s how bad hardware can manifest.

(Particularly given that a clean install of El Capitan 10.11 did not clear this.)

If it’s a failing hard disk drive, that can be swapped.