Well. Sometimes upgrading a PC from a specified line like eMachines or Dell can be really difficult and frustrating. PC Manufactures like to make specific parts and BIOS so you can't upgrade, forcing you buy their next line of PCs.
A quick search shows that the eMachines you listed is a older small form factor PC.
It doesn't support a discrete graphics card, and the motherboard chipset is no longer supported, meaning they are no longer making CPU's for this socket.
Even if you could purchase a new CPU, the motherboard BIOS would not support it and it may not work at all.
I hate to be the bearer of bad news, but it would be easier to simply buy a new PC.
Thankfully there are budget plans for PCs that keep them under $400, or...