The very first LGA 775 processors were the Pentium 4 5xx series. They were 32 bit only.
The second LGA 775 chips were the Pentium 4 6xx series and they had 64 Bit instructions. All Intel desktop processors since are 64 bit. So the Pentium 4 6xx, Pentium D 8xx, Pentium D 9xx, Core2duo E6xxx, E7xxx, E8xxx and Core2Quad Q8xxx and Q9xxx all have 64 bit.
64 bit drivers did not become necessary for most people until Windows 7 though. Windows XP x 64 was not a very good OS and it was hard to find drivers for. Only with Windows 7 and people running more than 4GB of RAM has 64 bit become commonplace.