"It is implied that the person (you) did not know it was raining because he/she(you) was sleeping (at that time)." A couple of sentences : 아침에 비 오는데 자고 있었어. 아침에 자고 있었는데 비 왔어. Or, 아침에 자느라 비 온 줄 몰랐어 although it reveals the subject didn't know that. -지만 is used in formal writing and 근데 can be used as "and" EDIT : 아침에 일어나니까 비 왔더라 works also.

"그런데(spoken:근데)" means "but" "~지만" means "~, but" so, you can use two of all. the only difference between "그런데" and "~지만" is that you can seperate sentences by using "그런데" and can make it together by using "~지만" cf) 아침에 비가 왔어. 그런데 너는 자고 있었어. (two sentences) It rained this morning. But you were sleeping. 아침에 비가 왔지만 너는 자고 있었어. (one sentence) It rained this morning, but you were sleeping. ("있었어" means "was/were ~ing") you can also use "~는데" as it has same meaning as "~지만" cf) 아침에 비가 왔는데 너는 자고 있었어.