Also to add, you may have to verify the BIOS flash version as well for processor support. Such as towards the end of the support of a motherboard they sometimes add support for newer processors. So if you have an early release board, you may need to flash the BIOS to have additional CPU support.
A college friend of mine was given a system that had an old AMD Athlon 64 3000+ 1.8Ghz single core which was socket AM2 and his ASUS motherboard stated that it would take a dual-core CPU, but he failed to read the fine print that stated that the flash version had to be say version 12, and his board was like version 4. I mailed to him a Sempron X2 2200 Dual-Core that I no longer needed as an upgrade for this board. He got the CPU and installed it andgot a black screen on boot and said thanks for a bad CPU as for it wont post. I asked him if he verified that his BIOS was up to date. I stated to install the old CPU back in and then flash it to latest, and then perform the CPU upgrade and this fixed the problem. He then appologized for the statement of sending him a bad CPU when the CPU was perfectly fine, and it was his BIOS flash version was out of date.
We need the exact motherboard make/model which is on the board somewheres or make/model computer that this board is in, also just as important is which Core 2 Duo you want to go with as for some boards will only support maximum of the E4xxx series while others will handle the E6xxx series etc. With this info we can give you a thumbs up or thumbs down for this install.
If this motherboard came with a Pentium 4 socket 775 installed dont be surprised if this motherboard can not handle a Core 2 Duo as for unfortunately many are out there that max out at either Pentium 4 HT or Pentium D, and this is more common in off the shelf computers where the motherboard was never really intended to take more powerful CPU's. BUT in some cases you can get lucky as for just like my friends motherboard it just needed a BIOS flash to get the Dual-Core processor support, but this was also a better brand ASUS motherboard and not an off brand like TriGem as is in the case of an old eMachine I have will not take any faster than a Pentium 4 2.0Ghz CPU and came originally with a Celeron 2.0Ghz, and wont take a Pentium 4 2.4Ghz etc because it was never meant to support a CPU upgade beyond a Pentium 4 from Celeron of the same 2.0Ghz clock speed.
