That is probably the E4300 Intel Core 2 Duo or the E6300 core 2 duo the E6300 is 1.86GHZ the 4300 is just 1.80ghz eithier way you will be fine getting any mico ATX lga 775 board I found this cheap Gigabyte board that will fit in that case.
Now you will run in to a little problem with the power button switch and lights but its not that big of a deal since the case is proprietary the connector for the panel is not universal. You can however just place the connector onto the new board in a way so that the power button will function or you can rewire the front panel all together.
Now before you do this I would make sure you know for certain its the motherboard Iwould test the RAM and PSU before you do anything also reset the Cmos battery. If there are multiple dimms in use 1 at a time to see if it will boot.