|1st, your problem is NOT due to a bad processor. |
2nd, the LGA775 board does NOT support the Pentium 3.
3rd, you realize that you have to reinstall Windows due to the motherboard change, right?
Why did you replace the board to begin with? Because it was rebooting? More than likely, there was nothing wrong with the board. The 1st thing you should have done was disable the "automatically restart" feature that's built into Windows. That way, instead of rebooting, the system would display an error message telling you what the problem is. You may have an overheating CPU, bad power supply, bad RAM or a software problem, but there's probably nothing wrong with the CPU or original motherboard.
Did you apply thermal paste between the CPU & heatsink? I can't tell which method should have been used without knowing exactly which CPU you have, but like I said, it is NOT a Pentium 3. It's probably a Pentium dual core & if it runs at 1.6GHz, it's most likely an E2140. If I'm correct about the CPU, you should have used the "horizontal line" method. If you used no paste at all, or spread it all over the CPU like frosting on a cake, that can cause rebooting as well. Here's the instructions: