"modern" as in processors being made today? No. Your board is an "old" board and has socket LGA775 and can only support processors that fit that socket.
Here is a list of processors that fit your socket: Intel® Desktop Board D975XBX2 — Supported Processors
The Q6700 mentioned by vsslo in post #4 above is a good choice.
Yes, a solution, if you want to be current with technology, is to purchase a new board, which requires a new processor (with new fan), which will require new memory, and so on.
Provide your current processor model number for more information.
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