To begin with, I would try to fix the bluescreen error. That being said, if you really can't for one reason or another, I would do one of the following:
From Ubuntu, try using a zip program or similar to "split" the file in to multiple sections, and then reassemble on the new machine - many zip programs allow you to configure how big you want the chunks. I can not be more specific as I do not know linux programs that can do this...
(I think 7-zip is only Windows, but I just read a link about a Linux port in the Ubuntu repository. You can try that, or possibly running in Wine - otherwise, try to find a linux program that does the same).
I think splitting is the best solution in your case. Other than this, Samba can be a bit of a pain to get working, so, I would recommend trying to install Filezilla server on your laptop, then downloading filezilla to the Ubuntu live and simply copying it that way (If you need any detailed instructions/guides, let me know).
Finally, the quickest solution, but possibly not recommended is if your old machine was a desktop, you can take out your laptops hard drive and copy it directly to there and then put it back in (as long as you are not using Bitlocker/similar).
Or... on the last solution, if you have a USB caddy of some sort, you can take out your old hard drive and connect it directly to your new machine.