The failed T-1142 is usually not a power supply problem, but it is important to test that first. Power supplies failed on early models built in 2002 and 2003, but have been good in those built since 2004. Usually the motherboard fails and that failure causes the power supply to go out.
Your memory, pci cards, cpu and cpu fan, optical drives and the like are usually good.
A number of motherboards by PCChips, MSI, FoxConn, EGS, and others are available. Just search by the processor you have and the memory used.
However when the mother board goes, your ability to use the eMachines hard drive is lost due to Windows. Windows will detect the motherboard has changed and immediately suspect you of piracy. You may have success with talking to Microsoft on the phone when the error comes up.
Otherwise, the eMachines motherboard is $159.95 plus shipping... and will allow everything to work immediately. I do not recommend this, but if you have to get to data quickly, this is one way that works.
In our opinion, you are ahead of the game to buy a copy of Windows, and a motherboard-CPU combo from
www.newegg.com,
www.directron.com,
www.tiger.com for less than $100 and start over... MSI, Gigabyte, EGS, FoxConn, Chaintech, ASUS... whatever... are all better than the eMachines board which has an incredible failure rate of well over 60 percent.