Is it possible to expiate the sin of abandoning prayer for years by paying a sum of money to a number of people so they may perform Hajj on my behalf, or is there another way to completely erase sins?

For someone who intentionally abandons prayer, sincere repentance (Tawbah Nasuh) and making up the missed prayers are required according to the majority of scholars. He must also repent from other sins by abandoning them, regretting them, and resolving not to return to them. If the sin involves the rights of human beings, then the rights must be restored to their owners. Sincere repentance erases sins and removes their effects, as Allah Almighty says: "Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.'" [Az-Zumar:53]. One should also increase in good deeds because they remove bad deeds: "Indeed, good deeds do away with ill deeds." [Hud:114]. It is not necessary to collect money to facilitate Hajj for others.