i'd say the ram is fine if it's booting every day, next time you start it find out what bios it has, should be on the splash screen when you first start it, if it doesn't say press either f2 or delete (should be one of these but also be f8) as soon as you start it up to get into it, also if you can try shutting it down as soon as it starts up and restart it as it could be a problem with overheating when it's been on for a while
could also be a faulty psu? i know it has an external power brick and an internal card that handles all the transformer gubbins which makes it harder to test, if you replace the brick and it's the internal part that's fucked then you've wasted money, if you just want to get you stuff off if i'd take the hard drive out and get a cheap usb enclosure then copy everything you want over to your laptop