This Mac had the same symptoms a while ago. Eventually, I couldn't turn it on at all. Later, I found that the hard disk was failing and the motherboard wasn't functioning correctly.
So what I really suggest is to back up all the data that you want to keep and then send it in. I've had to do this twice, and I've found that DVDs are the best for doing this, although I have a lot backed up on
A-Drive from my other crashed computer right now.
Anyway, what you can do is, download
keka, install it and then drag it to the doc. Next, put all your files that you want backed up into a folder. Check the size of the folder to see about how many dvds you'll need. Get a bunch, and then open keka. Change the settings to low compression or store, and tell it to split the compressed file into volumes (Enter a size that's a bit lower than the DVDs maximum; ie: 4 GB)
Stick a dvd in, and double click. Drag one of the volumes (that keka made) there and then click burn. Repeat until they all are on DVDs.
Then take your Mac in, and you won't lose your data. I hope you still have your installation disk for Mac OS X and other applications. If you don't, the apps can be backed up in the same way usually.
Alternatively, if you have a large usb drive and/or another computer, you could move the data onto there for storage. You'll need a USB drive (preferably large) to move it onto another computer.
I don't know if your MacBook has a DVD burner. You could use CDs.
If I'm not being clear, or you need more help, please ask.
**If your thinking to try A-Drive, you'll see why I don't suggest it. Limit 2GB capacity for an upload, and it takes about 10-20 hours to do that. 2GB is about half of a DVD
**The guy may be capable of recovering the hard disk for you. When you take it in, you'll probably have to pay to get the Hard-Disk replaced. Backing up the data is just something easy that you can do for free before it completely crashes