I'll hazard a guess that you're getting an interrupt from some of your add-on hardware and it's causing confusion - this happens quite a lot on Mediator equipped A1200s, for example.
Booting without startup-sequence is perhaps not initialising the hardware (eg: gfx card?), so you're not getting the interrupts, so WHDLoad works alright. No idea why it would suddenly start going like this though. Does it happen for all games or just a few ?
Unfortunately, if this is the problem, there's no workaround that I know of
