In the attached are two solutions (two buttons).
Since there are 80 or so files I looked for speed with Solution 2 below.
Solution 1 (slower)
The button runs the macro blah which opens each workbook one at a time and copies data from the first sheet.
It uses a plain cut and paste so if there are formulae in the ranges you're copying from you'll get them too (I think) as well as any formatting. If you want to be more specific about copying values and perhaps some formatting it shouldn't be hard for me to tweak the existing code.
Solution 2
This runs blah2 and only puts links (formulae) into your resutls sheet then converts the results of those formulae to plain values. It doesn't open the workbooks and so is considerably faster.
However, it does assume that the sheet you're copying from is called Sheet1. If they're not then a little dialogue box will pop up asking you to click on the correct sheet name, but if there are 80 files you'll be doing this a lot. which is tiresome.
So if (mostly) all the sheets you want to copy from have the same name, you can edit the blah2 macro, finding the line:
.FormulaArray = "='" & x & "[" & y & "]Sheet1'!" & are.Address 'insert a formula (link) to get the data from the closed workbook
and changing the red text to that sheet name, leading/trailing spaces included.
Should your first sheet names be not at all consistent, there is another way to get sheet names from a closed workbook which involves more code which I'll write if you really need it, otherwise it may be better to wait out Solution 1.
There is copious commenting in both macros for your information and your own tweaking.