Several things are unclear as to your situation. Was your status here before as a tourist or as a student (it might make a difference, depending on the status in which you were admitted). You need to speak with a lawyer directly to clarify.
If you overstayed, or were out of status in the U.S. before, you can no longer use Visa Waiver - you need to apply for an actual visa at the U.S. consulate in your country. In any event, Visa Waiver wouldn't be appropriate for study - only for a brief visit.
If you accrued one year of "unlawful presence" after the expiration of your visa and then left the U.S., you are subject to a ten-year bar to reentry. Staying abroad only three years wouldn't help at all.
It isn't clear, though, that you accrued unlawful presence - if you were admitted on a student F-1 visa, you may have been admitted in such a way that unlawful presence didn't start building up even if the I-20 expired. You need to discuss this with a lawyer.
Hardship in country of original,, what you have to offer the U.S., and the fact that your intent while here is to study would all be COMPLETELY IRRELEVANT in applying for a waiver of a reentry bar based on unlawful presence. The ONLY think that would matter would be a high level of hardship to a U.S. citizen spouse or parent.
Speak with a lawyer about your options.