No. Best case scenario, your system MIGHT be able to support a dual core processor of the socket LGA775 variety, like a dual core Pentium or a Core 2 Duo E4xxx series. A Core i3 is not compatible with your motherboard, the i3 uses socket LGA1156 and your Pentium 4 uses socket LGA775. I'll re-post an answer I gave to an earlier question:
There are some factors that you must consider when changing the processor in a computer. Socket compatibility, motherboard support and bios support.
Socket compatibility-
The cpu must be compatible with the motherboards socket type. For example, a socket AM3 motherboard will support most AM2, AM2+ and AM3 cpu's, but a socket AM2 motherboard will not support a socket AM3 cpu. Also, an oem (branded) system with a socket 775 motherboard WILL NOT support every socket 775 cpu.
Motherboard support-
If you're currently using a single core cpu, the motherboard might not support a multi core cpu. Motherboards that support quad core cpu's have more voltage regulation circuits than motherboards that support single and dual core cpu's. If you have a custom rig, this may not apply, since most current motherboards can support almost any cpu of the proper socket type. Some oem (branded) systems use a motherboard that will allow you to use a cpu up to a certain wattage, but not more.
Bios support-
For custom rigs this usually doesn't apply, but for an oem (branded) system you can only use a cpu that is supported by the system maker. For example, the system maker has a bios version for a motherboard that has a Core 2 Duo E5200 in it, but the system maker might not have a bios version that would allow a Core 2 Duo E8600 to be used on that motherboard. Some oem systems with a dual core can support a quad core, but in order to find out exactly which processors are compatible with your motherboard AND have bios support from the system maker you'll need to go to the system makers website to find out which cpu's can be used. If you try to use a cpu that doesn't have bios support from the system maker, either it won't work properly or it won't work at all.
EDIT
If your motherboard is in a custom rig and NOT a branded oem system, use this link. It lists all cpu's that are compatible with that board. You may need to flash the bios for certain cpu's, be careful there, if you lose power or your internet connection while flashing (downloading a new version of) the bios, it will render you bios chip inoperable, which basically makes your motherboard useless until you replace the bios chip. Again, be VERY careful if you need to flash the bios. Here's the link, select 'CPU Support List'.
http://www.asus.com/Product.aspx?P_ID=xs6iinKxu0y5agcg&content=specifications