Database usues/ application

yes.

run an sql query, pulling whole list into the result set, then get it to display all where all fields match.

My client manages 24,000 mailing addresses in an Access database. The software will only find EXACT duplicates the suggested way - meaning if one entry says "Street" and one says "St." they will not be flagged as dupes. That being said, it's still an excellent option. One can sort, update, filter and otherwise manipulate the data so beautifully in a database. You'll wonder how you ever managed with just a spreadsheet. Databases are SO useful!

Within a database, you can define what is a duplication by defining the key. It means that you can say that a "line" (a student in you case) is the same as another if (for example) the first and last names are the same or if you want to check the adress too or whatever you like..
There are also a good deal of tools that can set up the database from your excell file.

A database would be an excellent solution / upgrade. However, from your question it sounds as though you have never worked with a database. If this is so, then it is imperitive that you get solid and thorough training BEFORE you develop a database. And not just the mechanics of using a particular database product, but data design as well. Fixing data design problems after a database is built is very difficult -- think how hard it would be to "just" move your entire house ten centimeters farther from the street after it's been built, as opposed to changing the drawings before it's built.