I have put off returning to 18.3--when it runs, I like Mint 19--and after several false starts, I realized that when the screen opens to the blinking cursor, if I see the cursor jump down a space, that is the sign that it is not going to start.
Also, this morning for the first time.it seemed to be starting properly, went to the bootscreen offering a choice between Mint 19 or 18.3, and then returned to the black screen and stayed there.
Winter has arrived early and I am short on time.but I will probably turn back to 18.3 soon.

I have found a few threads like this on the Linux Mint forums. I recently installed Linux Mint 19 on my Acer Aspire 7560G. I installed the xfce version because it's an older computer. I currently also have Linux Mint 17 (17.2, I think) and 18.2 on the laptop.

Upon booting I found myself faced with a blank screen except for the cursor at the top left. It takes about 3 minutes to go from the blank screen to the login page.

Searches suggested it had to do with a kernel upgrade, but this was a clean install of Linux Mint 19 (I don't recall exactly which kernel version it was but it wasn't the 14. . . . -24 that others had problems with).

Once booted it runs fine. However, if the screen locks and I have to log in again, the same thing seems to happen and it just seems to be frozen, until finally the main screen reappears after about two minutes. I use a dual display and when the screen did finally reappear, it was like the monitors were switched. The menu appeared on my top (i.e. secondary) monitor but clicking on the start menu did nothing. I could only access the menu by clicking where the start should have appeared on my bottom monitor (which is assigned as my primary monitor).

When configuring the display, no matter which monitor I assigned as the primary monitor, the menu bar always appeared on my secondary monitor. I had to find a workaround to get the menu bar where I wanted it. Also, when changing desktop backgrounds, I noticed that the background tool referred to my secondary monitor as "monitor 0" and my primary monitor as "monitor 1" which suggests to me that it was confusing the two monitors.

Booting with the secondary monitor unplugged has no effect.

I've looked through the kernel log and found this message "[radeon]] *ERROR* atombios stuck in loop for more than 5secs" taking up the bulk of the load time, but when I read about the error I can't make much sense out of what I'm reading except that it seems to have to do with the built-in Radeon graphics driver. I've not others mention this in any of the few other threads I've read about Linux Mint 19 being stuck on a black screen for minutes after booting.

I had started with the conviction that this was a software problem, but--having finally admitted that I could be wrong--I returned the tower to the vendor, who within a few minutes declared that the SSD was wonky, and said he would replace it on warranty.
My apologies to everyone whose time I have wasted (I have already apologized to my partner, who has been telling to take it back for a couple of weeks!).