Not really.
If the problem is the power supply, that's a very easy fix.
If the problem is the motherboard, that's actually much easier to fix than you think.
Buying a new computer will be the most expensive and most time consuming option. You'll need to reinstall all your programs. Do you have the installation files? Do you have all the updates that you've applied over the years?
If everything else on the computer is OK, putting in a new power supply or motherboard is IMHO the most effective solution.
If you get the same motherboard that came with the eMachine, you'll be able to boot right up with your existing boot drive and all your programs will run just fine.
Thanks. Well I can get a new power supply and see if that works. I was hoping to get a slightly better MB because I would assume eMachines MB or fairly cheezy.
If I buy a different MB I will have boot or bios problems?
What if I buy new MB and CPU which probably means new RAM. The current CPU is a Celeron.