Leaking basement help

Ok this is my first post besides introduction. I have done alot of home repair in the past but foundation is something beyound me. I have a backyard that slopes back torwards my house. under my back patio is an old fruit cellar, inside my house this is located under my stairs. The backside of my house is an addition that was turned into a dining room. From what I have been told this used to be an old screened in portch. When it rains heavy this leaks around the door frame that leads you into the fruit cellar. To prevent this I put a new drain system in the ground that leads to the side of the house. To no prevail this has not fixed the problem and short of raising the back side of the house or adding a drain and tile system I don't know what else to do. Any suggestions to this issue would be greatly appriciated. I just bought this house this month so as to how long this issue has been happening I don't know but I'm sure it's been happening for a long time and has caused more issues. Below I've provided some pictures.

More photos.

Last photo attached. I want to finnish this basement due to my master bedroom is located down there but until this leaks fixed I'm affraid to invest anymore money. Thanks for all and any help.

We just covered this with another person, same type situation, here is the link. http://www.houserepairtalk.com/f32/water-infiltration-9672/
There are also others with other ideas, try the search engine up top. I'm not trying to push you off, these questions just come up alot.

No, I app you telling me that. I just googled this website since I was at a loss on what to do. I will check that link out and thank you again for the direction.

So I read that thread and I have gotten a est from Jerrys water proofing. They gave me a 15000-20000 est on a drain and tile system. My house does not have a sump pump in the basement. I can't raise the back porch since that fruit cellar is directly below it. They pored the patio dirrectly over the top of the cement roof of the cellar. I have a french drain running the side of the house and the gutter extension in my picture runs into it. I don't think a drain and tile system would help since the water is coming from above and not in on the floor. Someone had filled that area above the door frame with expandable foam and for the life of me I don't know why. The foam is a insulator not a sealer. Do you think that filling that fruit cellar back in and walling it up would help? The situation in the other thread was similar in some aspect but not in all. I have installed over sized gutters all around the house and also added that drain I put up against the house in my photo. If I back fill that fruit cellar and thus repoored that pation to slope away from the house, would in you opion help? Is there any type of sealer you would recommend?

Thank you for taking the time to help me. Have a great Thursday!

Well, the situation has the same similarities when we talk about treating the water levels as thought they are higher than the basement floor.

You basically answered all your own questions, you are thinking exactly like you should.
Remove the rootcellar creates a hole still into the foundation, the whole area needs to be dug up,just as you said. The waterproof companies will tell you you can just apply some tar coating, not true, that is what is called water dampproofing. You need a waterproof system installed if you need to get rid of the water.
Google waterproof foundations, there are plenty of options.
Hope this helped.

Yes it did. I guess I just wanted some confirmation on what I was thinking since I would not consider myself a professional on any level.