well just my 2 cents.

it's rather un-ethical to just leave your job suddenly (even though it's stated in ur handbook that you only required to give 24 hr notice or etc.)

try to negotiate with your current co. so that you can leave maybe in 1 mth time, so that the so-called biz impact is not severe

at the same time, try to talk with the new co. as well lor.

you are aware of the 2 mth notice beforehand rite, did you let the new co. knew about it?

just a word of advice, don't burn bridges ... the world is really small and it's getting smaller every day ...