If it has passed Dell logo screen, it has passed POST basic hardware test. Losing video after that can be due to video card malfunction (overheating or underpowered).  MSI VN210-MD512H is GeForce 210 low end card.  max power is 30W. 380 tech guide mentions HD3450 or GeForce 9300 GE (both 256MB card using DMS-59 connector).  The TDP is 22-25 W.  
Hi, bought a refurbished low profile MSI VN210-MD512H graphics card for my Dell Optiplex 380 SFF PC with the hopes of using dual monitors with it. Though when I go to boot the PC up, it only makes it past the dell logo screen before the display goes blank leaving the PC running. I have attempted to install the drivers and MSI utility but they require the GPU to be actually plugged in for the download. The PC is running Windows 10 Pro and what with the age of the actual machine and the new GPU, i wasn’t sure it would work, though this seems to be some sort of hardware error. It has a new motherboard, 8gb of RAM and the stock CPU and drive. I’ve never really worked with Dell PCs before, was hoping for some help on this subject please I have attached a picture of the machine and it’s new GPU bellow. Cheers, Josh.
Optiplex 380 SFF Graphics Card Issue