You must contact the manufacturer of the motherboard or system, and ask them which processors are supported by their bios. Then, you can select from those processors.
An upgrade processor must be socket, chipset, and BIOS compatible.
Just to set expectations, there is absolutely no way that you can use any Intel Core i3/i5/i7 processors with this board. Considering the processor that you already have, your only choices for a significant performance upgrade are going to be an upgrade to one of the Intel Core 2 Quad processors.
Now, the Intel Core 2 Quad processors require additional power. You need to ascertain, from the manufacturer of the motherboard, whether this motherboard has the capability to provide this additional power and, if so, which of the Intel Core 2 Quad processors are supported by the motherboard's BIOS. Note also that it sometimes requires a BIOS upgrade to enable this support - and, this BIOS upgrade must be installed BEFORE you remove the existing processor.
If you cannot upgrade to an Intel Core 2 Quad processor, there is really nothing that you can do to improve the performance of this system. It will be time to upgrade the entire system to something more modern. Considering how old this system is, you have many processor generations to pick from - but go for the latest that you can.
Hope this helps,