Kernel 4.18.0-14-generic Borks Display

Yesterday's apt update included the 4.18.0-14-generic kernel. On a couple of my Ubuntu 18.10 MATE laptops (older DELL and Samsung models . . . I can't recall the models; they're at a different location), when they rebooted, I was greeted with a blank screen.
Evidently something went awry with the video driver compatibility.

Anyone else experience a problem similar to this on older machines? I had no problem with my newer laptop (DELL Latitude E6530 running Ubuntu 18.10 MATE). Was able to work on both older laptops using the old Shift-key boot trick to get to the Grub menu's Advanced options and switching back to the machine's 4.18.0-13-generic state. Never had this happen before.

Guessing I'll have to wait until the next iteration of the kernel for a fix? Or is there something I can do in the meantime to "patch" those two older laptops? TIA.

[In response to the request for information about the graphics driver...]

$ inxi -G -M
Machine:
  Type: Laptop System: SAMSUNG product: R530/R730/R540
  Mobo: SAMSUNG model: R530/R730/R540 BIOS: Phoenix 
  v: 08JV.M029.20100621.hkk date: 06/21/2010 
Graphics:
  Device-1: Intel Core Processor Integrated Graphics driver: i915 v: kernel 
  Display: x11 server: X.Org 1.20.1 driver: modesetting unloaded: fbdev,vesa 
  resolution: 1366x768~60Hz 
  OpenGL: renderer: Mesa DRI Intel Ironlake Mobile v: 2.1 Mesa 18.2.2

$ inxi -G -M
Machine:
  Type: Portable System: Dell product: Latitude E5400
  Mobo: Dell model: 0D695C
  date: 04/29/2009 
Graphics:
  Device-1: Intel Mobile 4 Series Integrated Graphics driver: i915 v: kernel 
  Display: x11 server: X.Org 1.20.1 driver: modesetting unloaded: fbdev,vesa 
  resolution: 1280x800~60Hz 
  OpenGL: renderer: Mesa DRI Mobile Intel GM45 Express v: 2.1 Mesa 18.2.2

That's all I can provide. I don't know any other command magic to display graphics info.

Yes, I was also greeted with a blank screen on my veteran PC. I also switched to 4.18.0-13-generic state. I'm looking for a way to fix this.

This bug has been confirmed: Ubuntu boot failure. 4.18.0-14 boot stalls. (does not boot)

For now, I just deleted the latest kernel:

sudo apt-get remove "linux-headers-4.18.0-14-generic"
sudo apt-get remove "linux-image-4.18.0-14-generic"
sudo apt-get remove "linux-image-unsigned-4.18.0-14-generic"
sudo apt autoremove

P.S. Kernel 4.18.0-15.16 has fixed the problem. It is available in -proposed.