Old template to new template... about 400 times

[DavidExcel]

I have about 400 files in an old template. The data in each file needs to go into a new template.
Most of the cells between the 2 templates don't match (cell B7 in old template may go to cell C14 in new template, even in a different tab sometimes).
... I really don't want to do it manually 1 by 1.

I would like to build a Macro that does:
1- Open 1st file in selected folder where old template files are stored.
2- Open the blank new template.
3- Copy/paste the data between the 2 files.
4- Save the new template with a new name a selected folder.
5- Close the 1st old file.
6- Open the 2nd old file.
... Repeat until all old files have been transferred.

Has anyone done something like this before?
Any advice?

Thanks,