I downloaded the FreeBSD version 9.0 dvd iso image on my 64 bit machine, tried to burn it to a dvd, but it failed, and messed up my dvd. So I scp'ed the image to my old 32 bit machine (the beast), and used that machine to burn the dvd. However, the computer locked up around the time the dvd was almost finished burning, I figured it might have worked completed successfully, or maybe not. So anyway, I figured since I wasn't sure, the best thing to do is test it. So I rebooted my machine and it started booting from the DVD, and then successfully booted into the FreeBSD liveDVD. It took me a second to realize what exactly happened. My 32 bit machine just booted into a 64 bit OS! I checked executables that were running with the file command and it confirmed that they were 64-bit executables, uname also confirmed that this was the 64 bit version. I know that it is not a 64-bit processor, its a P4 with hyperthreading.
How is this possible? Is my computer alive?

There are P4 versions that are 64 bit capable,

How can I tell if that is the case? and is it at all different from a true x86_64?

/proc/cpuinfo (in Linux) says vendor_id = GenuineIntel cpu family=15 model=4 model name= Intel(R) Pentium(R) 4 CPU 3.00GHz

It is a true x86_64. Post the exact type of your CPU.

wikipedia -> List_of_Intel_Pentium_4_microprocessors

Look for "Family 15 Model 4" ->
with "Hyper-Threading" -> Prescott 2M -> Pentium 4 HT 630

"Intel 64" indicates a 64bit processor.