Normally running out of ram results in low memory errors, and is unlikely to happen at start up. No page file could account for the hiccups.
Its not the best idea to not have one in Win 10 as unlike every other version of windows, it treats ram differently and only uses Page file if its running out of ram. Win 10, instead of closing programs you have run since start up, compresses them into ram so they load faster if you start them again.
Problem here is if you have no page file, win 10 has no where to put these files if you play a game that needs most of your ram, and will crash. If you have lots of ram, Win 10 may never need to use your page file so its not just extra insurance for those times you do need all your ram. Better to let win 10 manage page file size... i have 16gb and page file could use up to 16gb if it wanted, its currently only using 347mb.
Can you get into windows? if so, Try running this:
right click start button
choose command prompt (admin)
type
SFC /scannow and press enter
this scans system files and may fix this behaviour
One BSOD isn't much to worry about, you can download and run who crashed:
http://www.resplendence.com/whocrashed
and it would look at log files except it can't cause you have page file off... oops, and isn't making the dump files who crashed needs to read to figure out cause.