Wow! Laplink is still around? I used it a few times maybe 30 years ago, when it needed a special cable that I had to make myself. Aside from that, the program worked well.
For me, the big question has always been this. You say you want to move some "old files and such". The first step is to determine which files need to be moved. If it is just data files (documents, pictures, music, videos, etc, plus folders that contain data files), then things are easy. Whiz a copy across the connecting cable, and you are good.
As soon as you try to move programs (also called applications, like Microsoft Word, Firefox, media players, DVD burners, and all other programs), things get really hard really fast. Instead of trying to transfer those, you should make a list of them, and then download and install them on the new computer from scratch. Get them from the manufacturer's web site they originally came from. If you paid for a program, be sure to jot down the license number, if any, so you can use it on the new computer.
The operating system (Windows 7, Windows 10, etc) is a whole 'nuther bag of worms. I wouldn't even try to do a file-by-file transfer. If I understand the situation, the old computer has Windows 7 installed, and you don't want to transfer that. The new computer has Windows 10 pre-installed and up and running, and you don't want Windows 7 from the old machine to overwrite it.
Bill M, Clonezilla looks like a disk clone program, meaning a program that makes an exact duplicate of one computer onto another, word-for-word and bit-for-bit. I don't think that is what you want to do here, since it would copy Windows 7 onto the new computer, where Windows 10 already resides.
Having said all that, there are some transfer programs that will let you transfer everything except the operating system. In other words, they would bring across the data files, and the program files. Perhaps Laplink and Clonezilla can do that, in which case they are a great solution.
If the copy program (Laplink, Clonezilla, opr whatrever) can't do this, then the procedure seems to be that you first start your new Windows 10 computer, and figure out what programs (applications) are already installed. Then download and install all the other application programs you want to end up with. Then, connect your Laplink cable, and find and copy the data files from the old computer to the new one.
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WARNING! I am not a computer jock. I would be perfectly happy to be corrected about anything I have said, or misunderstood. In fact, I find myself in a similar but kind of opposite situation. My computer is running Windows 10, while my wife's computer is running Windows 7. I need to grab a copy of Windows 10 from my computer and install it on hers, without disturbing any of the programs or data files that she currently has. Once Kidkraz's issue is resolved, I would love to have some advice on mine.
Bill