Flash the CMOS and you are going to find that the 915 chipset does support chips the Intel® Core™ family of processors (socket 775) like this Intel Core 2 Duo E4600. The earliest chipset for support of the Intel Core family of processors would have been some of the 945 chipset based boards.
You are correct about the 945 chipset but the 915 is even older than the 945 if I am not mistaken and only supported Pentium 4 and Pentium D chips. Now through BIOS revisions I know quite a few motherboard manufacturers made some older chipsets work with newer CPUs than they were designed for. That was common in the early LGA 775 era. That was really only common with the big manufacturers though like Asus and Gigabyte.
I seriously doubt EMachines would have released a newer BIOS with additional CPU support for that board. My very strong suspicion is that your new CPU is not compatible with your motherboard. You just can't assume a CPU will work with a motherboard especially with LGA 775.
I agree with anort3, I think that that board only supports Netburst CPUs, if even all of their LGA 775 models. It's like trying to run a Bulldozer FX CPU on an AM3 board or an AM3 CPU on an AM2+ board or an Ivy Bridge CPU on a 6x series chipset board. It'll work with BIOS updates, but OEMs rarely have such updates for their machines.