New build, trying to recover files from old hard drive - need help!

You didn't say if your new system is Windows 7 or 10? 32 bit or 64 bit?

In any case, if you have the old HDD plugged into the motherboard as a second hard drive, you can see it in Files Explorer [Windows Explorer] probably as drive D if you do not have a DVD/BluRay drive installed on the new system.

Just make sure that you go into the BIOS and in the Boot menu, disable the old hard drive from the boot menu item, and only have the new SSD drive as a boot device [Disable everything except the new SSD drive]. Otherwise if you add the old HDD after installing Windows on the SSD, and you leave the BIOS at its default, it might cause problems and try to boot from the old HDD, which will very likely give a Blue Screen.

What I've done in the similar situation in the past is on the old hard drive, delete the Windows directory, Program Files and [if it's 64bit], delete the Program File (x86), ProgramData, and every other folder except for the "Users" folder.

Then I go into the "Users/my user name" folder and copy the Documents, Music, Photos, Videos, Downloads, into a new folder on the old HDDs main directory. But I first create a new folder on the old HDD and name it something like "Backup", and copy those folders above, to that "Backup" folder.

For all my old emails [I use Thunderbird], email settings and email accounts, I simply copy the "Profile" folder which is in the "D:\Users\your user name\AppData\Roaming\Thunderbird\Profiles" folder [replace the "D" with the drive letter of your old HDD].

Simply copy the Profiles folder to the main folder of the old HDD. Then, from the new installation I point Thunderbird to that folder from the Thunderbird "Help menu > Troubleshooting > Manage Profile" [something like that, I'm going by memory]. Now I have all my emails and email accounts exactly the same as I last left them.

After I am happy with copying anything else I want to keep from my Users folder on the old HDD to the main directory of that drive, I then delete the old Users folder and anything else that's left from the old Windows 7 installation, and only keep those new Back up folders I made [above].

Any program or game I installed on the old HDD I simply download again, or find the installation files from the old HDD Download folder, that I copied to the Backup folder. Easy Peazy

I hope this makes sense.