If you are transferring files from one computer to another in the same building, you do not want to use the Internet to do it. You don't need an Internet connection unless your new PC needs to activate Windows.
If you have a wireless router as part of your Internet connection, and your new PC has an Ethernet port, connect the Ethernet port to the router with a normal Cat 5 or Cat 6 Ethernet cable. In fact, if the old computer also has an Ethernet port connect that to the router by Ethernet as well. That should be more reliable and faster than using WiFi.
You don't say what operating system the old computer is running, but I would guess that it is possibly Windows.
The next step is to allow file sharing between the computers. It is probably easier to allow the old computer to share files and then in File Explorer on the new PC map the appropriate drive on the old computer as an extra drive on the new one. Then you can copy files and folders from one machine to the other from within File Explorer running on the new PC. This should be far faster than any solution that puts files onto Cloud space on the Internet, and then copies them back off again.
There are other alternatives including using a USB connected external drive as an intermediate transfer medium, or temporarily removing the drive from the old PC and installing it in a USB connected external disk enclosure to the new PC.
Personally, if you don't already make regular backups (as you never know when a disk drive might actually fail), I would recommend getting an external USB disk drive (I use a 2 terabyte drive) and using that as a transfer medium dumping the files you want to transfer on to the external drive from the old PC and then copy them on to the new PC. Afterwards you can use the external drive to keep regular backups of your important files.
Please be aware that while personal data files such as Documents, Music, Pictures and Videos can be copied, games and programs may not work if copied and may need to be installed again on the new PC. Sometimes you can copy games data once the games have been installed from their original installation media, but sometimes it is not straight forward and you might need to seek advice from the games company about transferring games. Some software may need relicensing if it is installed on a different computer.
I hope this helps.