Old machine has XP.
The plan will probably be:
1. Buy a new machine probably with Vista Home.
2. Take old HD (drive) out of old eMachines put in an enclosure that has a USB plug about $25??? (is this how to do it?)
3. Plug in USB into new machine to access old programs and files on the old hard drive????
Does this make sense? Can I run the old programs?
No. You have to install the programs in order to run them unless they are old DOS programs.
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Might think about an eSATA linkup ...much faster than USB.
If your drive was SATA.
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.