Can Dell Dimension 6400 run 64-bit Win7

There is no Dimension 6400.  There is a Dimension 8400 desktop.  Is this what you have?

The Dell downloads for the 8400 are ONLY for XP.  Dell does not support any device drivers for Vista or Windows 7, thus if you install Windows 7 you are "on your own" to try and find all the needed device drivers.  Windows 7 will install many drivers but as your 8400 (assuming that is what you have) requires a Dell sound driver, if you get everything else working you will probably have to do what others with unsupported sound devices have done, install a separate Windows 7 compatible sound card.

Unless you have more than 4GB of RAM (and again the 8400 won't accept more than 4GB) there is no reason to use the 64 bit version.  Stay with the 32 bit version.

There is an Inspiron 6400, which is exactly the same as an E1505 like I have.  It does support Windows 7 32bit using Vista drivers, but no drivers exsist for 64bit.

Duh, I don't know where my head was.....  I have a Dell Dimension 4600. I also have an Inspiron e1505 that I was hoping to put win7 64-bit on.

I will be doing a lot of work with Photoshop cs5 and while I have 3.25 GB of RAM in the Dimension now, if the install worked, I was planning on getting more memory.  Same for the Inspiron.  Sorry about the goof up.

You are limited to 4GB of RAM in the 4600 so there is no need for 64 bit OS.  The 64 bit OS will not work any better than the 32 bit with 4GB or less of RAM. 

Dell does not support Vista or Windows 7 on this model so the same comments I made about the 8400 also applies to the 4600.

Dell has Vista 32 bit drivers for the E1505 and some of these will work on 64 bit however according to the Dell manual, 2GB of RAM is max thus there is no use to install a 64 bit OS.