Your primary concern when going from 32 bit to 64 bit is unmanaged code. The default modules and the framework itself does not contain any unmanaged code, however, you may be using a third party module/component that does depend on unmanaged code (this would be in the form of a dll in DNN modules/providers, via references). Where I would start looking is in my bin folder as well as my installed module list first to see if you can find the culprit (only if you are using third party modules/providers). I would also verify that your new application pool is used only for the site you are trying to migrate to 64 bit (and thus, not being used by other sites in IIS that may not be 64 bit compatible, plus the isolation will be good during this migration). 

If you have no third party modules, or you find out there is no issue, I would then check to see if IIS is setup for this properly. In 2003 Server, keep in mind that .NET running in 64 bit was an after thought. While somewhat out of date but still on this topic, you can check an old blog post from Tom Kraak with his view a few years back on DNN 4.x in 64 bit on Windows 2003. He was also struggling with the machine running .NET 1.1, so perhaps it doesn't apply here but this post and his blog post should give you a few places to investigate and go from there.