If you got Microsoft Office via a download that presumably means that you actually downloaded a 'setup' file and then double-clicked on it to start the installation. That setup file might still be in your 'Downloads' folder (or wherever else you stored it). If so, you can probably copy it to a USB memory stick and then to your new laptop, and run it again to start the installation. However it's likely that you'd then be required to enter the registration code which you needed first time round, which might be a problem.
However (even if you didn't write that code down) you might be able to access it anyway. On your old laptop, download, install and run Belarc Advisor:
http://www.belarc.com/free_download.html
That collects together masses of data about what's on your machine,
including all of the registration codes for all its software.
If you finally have to admit defeat, consider using Apache OpenOffice instead. It's at least as good as Microsoft Office:
https://www.openoffice.org/
(I use Microsoft Office on my desktop, simply because it was there when I bought my computer secondhand, but OpenOffice on my netbook, with no problems whatsoever).
However if you use OpenOffice you should note that it's best to change the default 'Save' settings, so that OpenOffice automatically saves documents in Microsoft's formats, rather than in its own. (It's a simple one-off job):
http://voices.yahoo.com/how-set-openoffice-writer-save-as-microsoft-11017880.html