You want to get some data from a defective laptop and transfer it to the working laptop right?
You need a USB flash drive, with a size that's enough to store all the data you'll get from that defective laptop or better use an external hard drive...
Once done, insert that bootable usb you made and boot from it and select TRY Ubuntu, and you will be running on LIVE CD mode
Now you shoud be able to see the hard drive of your laptop and do what ever you want on the folders or data on it. It's time for you to copy those data on your external hard drive.
BUT... if that defective laptop is dead as it wont boot at all, you have to remove the hard drive and plug it on your working desktop/laptop and hope it will recognize it, then do the same steps above.