How to get ROW_NUMBER() in MySQL

There is no ranking functionality in MySQL. The closest you can get is to use a variable:

SELECT t.*, 
       @rownum := @rownum + 1 AS rank
  FROM YOUR_TABLE t, 
       (SELECT @rownum := 0) r

so how would that work in my case? I'd need two variables, one for each of col1 and col2? Col2 would need resetting somehow when col1 changed..?

Yes. If it were Oracle, you could use the LEAD function to peak at the next value. Thankfully, Quassnoi covers the logic for what you need to implement in MySQL.