Your old laptop still boots? If it does just copy your files onto a thumb drive.
I like to create folders on the thumb drive ,or whatever media I'm using, for each category, like "Desktop", "Documents" etc and then copy each group of files into their respective folders on the thumb drive. That makes it a lot easier for you when you're putting them onto your new computer.
Then plug the thumb drive into your new computer, open each folder successively, "Select All" and Copy/Paste from your thumb drive to the appropriate folder on your new computer.
There's also the Ethernet Crossover cable, like this one,
Belkin 10-Foot CAT5e Crossover Molded Networking Cable, just connect the 2 computers, run your network setup wizard and copy your files over.
If your old one won't boot, then trying an external enclosure is a good idea.
The first two methods will/should avoid the Permissions/Denied access issue but this one will not. You will almost certainly have to take ownership of the files once you connect the drive via external enclosure, so you might want to read up a bit first.
There are lots to choose from but here's my favorite,
Thermaltake BlacX ST0005U This one provides connections for eSATA and USB 2. They also make one that uses USB 3 but without eSATA. They'll all accept either a 2.5" or 3.5" drive. They're more expensive but I use mine all the time for file transfers, imaging our laptops and I even boot a complete install of Linux Mint from it.
