Q:

Windows 7 64-bit installation from alternative media (no DVD/USB Flash drive)

Greetings
I currently have Windows 7 x86 installed on my computer.  I want to install Windows 7 x64 on a different partition on my computer.  However there is a little issue, I cannot run the x64 install from Windows 7 x86 which I currently have. 
I was planning to Install Windows 7 x64 on another partition to then boot up from that partition to install it on the partition I actually want my OS on.  Once that is complete I could just format the partition from the Windows 7 x64 that I didn't need anymore.  But the installer will not run from the x86 version of Windows 7 even though I do not want to upgrade that Windows directly. 
The reason I'm doing this in such a weird way is that my optical drive is broken and I'm really not into buying a new one since I would use it like once every year or so.  I also don't have a USB Flash Drive which is big enough to hold the installation files. 
As far as I'm aware I cannot use an external hard drive such as this one, which I do have.  Are there any alternatives in which I can install Windows 7 x64 or am I forced into buying a USB Flash Drive or  new optical drive? 
Thank you in advance for your replies. 
Edit:

This picture shows my current partitions on my laptop.  I want to get Windows 7 x64 on the C partition but have to install it first on the F partition to then boot up the F partition windows to format C and install x64 on that one.  My external drive is J.
Edit 2: No alternative computer which has a DVD drive, install files are located on an iso from MA3D. To install my 32 bit version I mounted the ISO in Daemon Tools to replace my Windows Vista but since I cannot run 64 bit into my 32 bit OS this doesn't work. 
Edit 3:

Following this guide the above screenshot shows me another problem.  I cannot update my USB external HDD with BOOTMGR compatible code because I'm on x86 Windows 7.  Seems I'm forced into buying a new optical drive after all. 
Edit 4:
I'm going to try to create the boot HDD with the setup files in a virtual machine with the x64 windows 7 installed. 
Edit 5:
Solution in my case: Installed a virtual machine with x64 then made the USB external into the boot device and installed it.  So this solved my problem. 

A:

You can "burn" a Windows 7 .ISO to a USB drive & install from there, http://store.microsoft.com/help/iso-tool. 
AFAIK, so long as Windows (your BIOS actually) can see your Passport - as a boot device, you should be able to use that.