I'm using BOINC Manager Version 7.2.42 (x86) on Linux Mint 17.3 Cinnamon 32-bit.

BOINC runs fine at boot and will keep going fine if I don't mess with it. If I exit it, I can't start it again properly. The manager screen opens, but it says Unable to connect to the core client, or in advanced view it is disconnected, and doesn't show any projects that I'm connected to, no work units run. The options in computing preferences are incorrect, too, after exiting and restarting, though everything shows up and runs fine if I just let it keep running after it starts at boot time.

I installed it quite a few months ago now, and hardly remember a thing about what I did. I'm running a variety of World Community Grid things, and normally they all work, when I just let it keep going after boot.

It seems like it is finding configuration files at boot time, but not when I run it after booting. I don't know why.

I have same problem with Mint 18.1 and other previous versions.

If I stop boinc from task bar all is fine, it will restart, If I close from applet bar icon I get close and remember this setting check boxes, it won't even restart if I use those.
But I still see 100% CPU use after about the time I set in "start 3 min after system idle" . so it appears to be running in background even though boinc is not running.
Boinc is not running as far as I can tell. Not sure how to shut it down permanently if there is a terminal command to shut it down completely I would like to know.
I can always restart PC and then restart Boinc manager from programs menu.

I've looked in the system monitor while BOINC is still running after booting up. It appears all processes but the manager are running under a user name of "boinc", not my user name. I guess that trying to run it under my own user name won't work, then. Not sure how to run a program as "boinc". Doesn't appear to be a user I can log on as.

The normal situation is for the user "BOINC" to run BOINC and its applications. This user normally has similar privileges to yourself, but has special access to bits of the BOINC environment.
I too run Mint 18.??, and have had the occasional issue with BOINC not properly resuming its GUI so what I do is start it, then minimise it which is a bit of a cludge, but it works. For the most my Linux computers pretty much look after themselves as I have to drag a screen to them to get at the GUI (I've not tired any of the remote GUIs yet - that's on my TUIT list)