What do I do if I am asked for a purchase date more than 3 years ago, and I do not have the record of it, and it is not on the payer's website?

If you know you have held it more than a year enter any date more than a year ago. If you bought shares at different times enter “various “.

You should be able to contact the brokerage firm by phone to find out the exact date seeing that it is only 3 years ago. 

If you do not have record of the date, you will need to estimate as closely as possible to the date, but having the exact date is always best.  Since it is 3 years ago, it will clearly be a long term transaction so the exact date being a few weeks off will not have any affect on your return.

If you were trying to figure out if it was just under a year or over a year, this could potentially affect your return as it would be the difference between long term and short term.