There is no way I could ask him/her under the circumstances.
He/She was just too busy for me to ask him/her to do me a favour.
I really didn't feel I could ask a favour under the circumstances.
「とてもじゃないけど頼める状況ではなかった。」= There is no way I could ask him/her under the circumstances. / He/She was just too busy for me to ask him/her to do me a favour. / I really didn't feel I could ask a favour under the circumstances.
例文:
there was no way = とてもじゃないが
ask, ask a favour = 頼む、お願いする
under the circumstances = この条件の下に、そういう状況下
too busy = 忙しすぎて
feel = 感じ(る)