I doubt cookies affects it, or at least not the cookies you are talking about.
Need more info. Not tech savvy in this way. Im a console gamer and many members of my family are trying to be computer gamers.
Secondly, can one play amnesia dark decent with integrated graphics. She bought with out reading system requirements (EPIC FAIL) can it be jurry-rigged or do we need hardware to play it?
Maybe. On the store page it says this:
Graphics: Radeon 9600/GeForceFX - Integrated graphics and very low budget cards might not work.
So, depending on how good her integrated chip is she may be able to play it. If you're concerned about it you can contact Steam for a refund. They only give refunds if you haven't installed the game IIRC.
When you say it is asking her to input a new password each time are you talking about Steam Guard? If so I'd recommend going to the Steam forums, I don't have much experience with it myself but someone there will probably be able to help you.
EDIT: It seems like people haven't been able to find a fix for this, at least at the time this thread was created:
http://forums.steampowered.com/forums/showthread.php?p=22124850
I'd try starting up a new one and seeing if anyone has an idea of how to fix it.
EDIT2: Have you tried just turning off Steam Guard?