If you have not already installed the new install, you may be able to go back in Safe Mode and log on if you can do that.
Then do this. If you can create a new folder, most like can,
I will give you the most easiest way to do this
Go to your User folder
C:\users\YOUR NAMED FOLDER
inside that folder create a new folder and name it My Back Up
Then put any files that you want from your User Folder and your public folders>C:\Users\Public into that new My Back Up folder
So highlight/select all your folders as shown in photo
Then right click on any highlighted folder and select copy
Then double click on My Back up and open it
then right click on empty area and select paste
It may take quite awhile to copy it all in to My Back Up.

Now, I do not know if you have a DVD or BR Player or an additional hard drive connected inside or a USB external HD or a USB Thumb drive.
Now you are in safe mode, so I am not positive, on a Thumb drive, DVD drive or external USB HD, because in safe mode not all drivers load or the system may not recognize the thumb drive or USB drive when plugged into USB port, and DVD Might not work due
to possible issues, But I know with an internal IDE or SATA HD you should be able to now copy that My Back Up folder to the other location, which ever one works the best.
But first, you need to right click on My Back Up that you just copied all your data to and select properties.
It will load all files and subfolders and will display the total size of the folder.
Now the location you are copying to needs to be just a tad bigger than that folder size..
Depending on the size you are saving, will really also determine what you want to copy it to.
Thumb drives are cheap and you can get ones very large in size like at Walmart, Best Buy, etc.
A DVD will hold about 4 GB of data.
A BR will most likely be big enough
A internal hard drive is best option
and Thumb Drive or external USB HD may be your only option, if the system can detect them in safe mode.
So get the size and then let me know what it is.
In your My Back Up folder, you can open it and copy certain folders at a time to fill up a location device and copy more into other location devices, such as needing maybe 3 8GB thumb drives if your My Back Up folder was approx. 22GB total size.
So you do not have to copy all the back up folder together to a new back up location.
then after new install, insert that device with the Back up files and move them to your new user folder. Do not replace the system folder for system folders such as, you copied all the highlighted folders and everything inside them to My Back Up folder.
So to copy the files back. open each system folder and move all the files inside to inside that system user folder on new install in your C:\users\Your Name folder.
Be sure to format Thumb Drive FAT32 or USB drive to NTFS