You will most likely have two problems based on what you mentioned- both of which will result in failure.
First- the 32 and 64 bit operating systems come on seperate media. There's no way of doing a 64 bit install from 32 bit media (that i'm aware of) or vice versa. Also the keys are 32/64bit specific.
Second- the laptop has an OEM key, but any media you would probably have access to would be retail and the media is usually locked down to a specific kind of key. It's strange and annoying, but you'll need to get your hands on the correct kind of media to match the key that is on the laptop. It is possible to manipulate some files on the disc to change the keytype that will be accepted, but it's quite annoying.
Your best case scenario would be to get access to another OEM windows disc that matches your machine's key type 32/64bit.
(I'm not sure on if the following is appropriate to post on the forum- so the moderator can feel free to erase it)
My company uses exclusively Dell equipment, however my personal stuff is always Thinkpad

, and it seems like the installation discs that come with a new dell pc are just vanilla windows discs with some dell drivers preloaded. I don't remember if we've ever used them on a non-dell machine, but if you have a friend or coworker who recently bought a dell, that may be a way to gain access to a windows disc that could work for you.
I also- just realized you mention it's a work computer. If your workplace has an IT dept, it might be a good start to see if they have any windows discs that would fit the bill.