Yeah, my BioMenace used to hang at the loading screen as well, and as weird as it sounds, the fix was to move your mouse. I guess it was getting stuck waiting for a hardware interrupt or something. You could also start the game with your mouse unplugged of course.

As for OMF, it used to give me a "not enough memory" error until I got rid of all my TSRs (basically a "clean boot"), as it had a very high conventional memory requirement, almost close to 600k if memory serves me right. Actually even BioMenace had a high conventional memory requirement. It wasn't until few years later that I learnt that there was no need to get rid of all the TSRs, you could just tell DOS to load everything in the High/Upper memory areas by tweaking your CONGIG.SYS and AUTOEXEC.BAT. Not sure if this was something that was introduced in later versions of DOS or if it could do it all along. But it wasn't in any of the official manuals at the time, I found these tweaks in a game guide on some random BBS.