Formula to pull data from one sheet and column for another sheet.

Hello,

I have a spreadsheet and I am pretty sure that there is a way to do what I want but I am not sure how difficult. Sheet "student worker pay" has multiple formulas that work off of the data in column b. I was wondering if there is a way to have column B automatically fill in based on sheet "student worker list" column B?

The problem will be, sometimes, there will be entries of the same student on "student worker list" but with different dates listed in E and F. They will have a different ID # though. Is it possible for "student worker Pay" to match say cell A13 to column A in "student worker List" to find the row then use g13 on "student worker pay" to make sure it is equal to or falls in between column E and F on "student worker list"?

=IF(AND(A13='Student Worker List'!$A$2:$A$1500,G13>='Student Worker List'!E2:E1500,G13<='Student Worker List'!F2:F1500),MATCH(B2,'Student Worker List'!$B$2:$B$1500,0),"")

This is the formula I tried and when I use the Evaluate formula feature, it never matches A13 to the correlating cell on student worker list. I entered the formula in B13 to test it.

Any suggestions? If it is too much work, just let me know and I will manually check every time I input a new entry. I just figured this would save time.
Test Spreadsheet.xlsx

I attached the wrong file, but it's not allowing me to upload the correct file. I will try again in a bit.