|If you posted the model of your emachine computer we might be able to help you. You will most likely need to buy a restore set if it is still available.|
I am not familiar with the MyBackup software but if it created a full backup then you should be able to restore it back to a new hard drive. Your problem is with the motherboard.
By the time your replace both the hard drive and motherboard and most likely the power supply that probably took out the board you will have spent more than the cost of a new computer. I suggest you consider buying new. After that you should be able to recover your personal files from your external drive.
The link below is to emachines support.