I am 15 years old and I work for my dad on his computer, fixing stuff for him, etc. At what amount of income do I need to start paying taxes?

Are you on your father's payroll? By law he must begin deducting for taxes, workers comp, that type of thing at an income level.

It's not what he's handing you for helping - it's what HE's declaring he's PAYING you that counts.

I would guess he has an accountant?