^ Your motherboard will not support these CPUs. The best CPU you can get is a Pentium D series. The motherboard has an Intel 865G chipset and will not even support Core2Duo at all. You can use LGA 775 Pentium 4 5xx and 6xx series as well as Pentium D 8xx and 9xx series CPUs only.
Don't waste money trying to upgrade this board. These chips were not even very good new and they have been obsolete since 2006.
Edit: Extreme Edition processors of this generation had an unlocked multiplier for ease of overclocking. They are still hopelessly outdated. Even the highest end, fastest processor of this generation of chips is slower than a modern ~1.5Ghz netbook processor.
As I stated above the Pentium D models are the best you can get. The Extreme models are only Pentium D chips with an unlocked multiplier for overclocking. Unless you have aftermarket cooling these are useless to you. I don't really have time to browse ebay. Just look for the highest clockspeed Pentium D 8xx or 9xx series chip you can find. Example Pentium D 840 or Pentium D 960 etc.
No there is no quad core CPU compatible with your system.
I will add again upgrading hardware this old is throwing away money. Save that money for a new system. Truthfully a dual core 1.5Ghz Atom netbook processor will run circles around a dual core 3.8Ghz Pentium D.
Moore's law. Computing power doubles every 18 months or so. Pentium D chips were obsolete in 2006.