Did you go to an Apple Store or an affiliate? Better odds with the Apple Store.
I guess you didn't get the AppleCare insurance? Although if you'd been able to take this MB in at once it might still have been under warranty.
There are a few things you could try.
Kernel Panics can be caused by defective RAM, or a blown logic board, a bad USB peripheral (probably not on your MacBook unless you've had a mouse plugged in all this while), and just possible a bad hard drive.
The very first thing to do is take out the RAM and re-seat it.
Just being not-quite plugged in can cause an error. Doesn't happen often though.
It would be better if you could find, even borrow, the correct RAM sticks from somebody.
That would quickly verify if the RAM was the problem.
Working with RAM requires you use precautions against static.
It's easy to get a (cheap) copper ground strap bracelet for this and run a wire to your copper plumbing.
Or go nuts and hammer in a ground rod outdoors, $10 at Menards. Run the wire to the rod.
I'm not going to recommend using the ground plug on your electrical outlet because
a) I like you, and
b) I don't want you to die if you plug the wire in wrong (which is why even I mention it at all).
The bracelet makes sure static can't build up in your body and fry the RAM.
Just pop the RAM out, rub the gold contacts gently with a pencil eraser, brush off the crumbs with a cotton swab, and put it back in the slot.
Come to think of it, if you have an Apple Store locally, you could ask the Genius to do this. They get paid to help people, not run up repair bills.
If reseating the RAM doesn't work the HD is next. A bit more challenging, but new HD's are not expensive.
You'd need the right Torx screwdrivers. A printed guide for your MB, and some tape to stick the screws to the printout as you take them off.
That way you know exactly where to put them back.
If it's neither the HD or the RAM it would have to be the Logic Board somewhere.
BTW, any further details on where you took the MB and what they said would be welcome.