Random computer crashes since new Graphics card (No BSOD)

Run for awhile as you have it setup now, without the Microsoft basic display adapter, see what happens.

Try another display with HDMI/DVI/VGA if you have more problems. Best not to change more than one thing at a time.

No mini dump in the zip. Event viewer log does indicate a BSOD on the 3rd:

Attachment 242342

but C:\Windows\memory.dmp is no longer available either.

No idea about the PCI slot. Probably about the same odds as the mother board being bad I guess.

Maybe time to consider doing a Repair Install. Even though this will supposedly not mess with your files I would do an image backup first:

Repair Install Windows 10 with an In-place Upgrade

The first thing you need to do is backup your current install. The best way to do this is to use Macrium Reflect Free to make an image backup to an external hard drive. If you don't have an external hard drive now is a good time to get one as regular backup should be a part of your normal process. You can get a 1TB external hard drive for $60 (less if on sale).

I think the system is crashing (restarting) before the mini dump or memory dump can be created.

Code:

Event[422]:
  Log Name: System
  Source: User32
  Date: 2019-08-05T16:30:08.790
  Event ID: 1074
  Task: N/A
  Level: Information
  Opcode: N/A
  Keyword: Classic
  User: S-1-5-21-1742859438-2548898130-462100011-1001
  User Name: AWESOME-BUBBLES\Jason and Kristin
  Computer: Awesome-Bubbles
  Description: 
The process C:\Windows\System32\RuntimeBroker.exe (AWESOME-BUBBLES) has initiated the restart of computer AWESOME-BUBBLES on behalf of user AWESOME-BUBBLES\Jason and Kristin for the following reason: Other (Unplanned)
 Reason Code: 0x0
 Shutdown Type: restart
 Comment: 


Event[510]:
  Log Name: System
  Source: Microsoft-Windows-Kernel-Boot
  Date: 2019-08-05T16:39:23.799
  Event ID: 20
  Task: N/A
  Level: Information
  Opcode: Info
  Keyword: N/A
  User: S-1-5-18
  User Name: NT AUTHORITY\SYSTEM
  Computer: Awesome-Bubbles
  Description: 
The last shutdown's success status was false. The last boot's success status was true.

Event[527]:
  Log Name: System
  Source: Microsoft-Windows-Kernel-Power
  Date: 2019-08-05T16:39:26.904
  Event ID: 41
  Task: N/A
  Level: Critical
  Opcode: Info
  Keyword: N/A
  User: S-1-5-18
  User Name: NT AUTHORITY\SYSTEM
  Computer: Awesome-Bubbles
  Description: 
The system has rebooted without cleanly shutting down first. This error could be caused if the system stopped responding, crashed, or lost power unexpectedly.

Nothing in the Event Viewer log indicates what the actual cause of the fail is.