The fact that 32-bit Vista Premium came pre-installed with the system (called and OEM version) does not really make it much different from a normal retail full installation copy. It has all the same features and functions - in that there is no difference to my knowledge - it is not a "Lite" version (do you have any reason to believe your version of Vista is any different from the standard retail version and, if so, how is it different?). There are differences in the licenses - you can only install that copy of Vista (using that Product Key) on the same machine it came installed on and never move it - no matter if the computer totally dies. Plus pre-installed versions typically come with Recovery Disks and/or Recovery Partitions (not many companies provide genuine Vista Installation disks with new computers these days unless you absolutely insist on it and are buying directly from the manufacturer - and even then it may not be permitted or they may charge you for it (if not the full price, at least some amount) and they usually include the specific drivers for the hardware installed on that particular system and may include other software from the manufacturer or from 3rd parties who either provide free versions as part of an agreement with the manufacturer or trial versions that last for a certain number of days or a certain number of uses before you need to purchase them if you want them to continue to function). But as I said, I don't believe Vista is any different than the retail version. Now if you change Vista to 64-bit or upgrade to a different version, there may be some (with just a bit change) or many (with a version change) differences - but that's because of the change in the operating system, not because of how or where it was installed. But in any event, it doesn't really matter what version it was (especially if it's the one that came with the system) because the image you have is of whatever was installed and that is what will be restored when you use the correct restore procedure.
As far as Laplink DiskImage Professional goes (I assume it is
Laplink® Software - Diskimage Professional - Laplink DiskImage the best way to protect your data from being lost unexpectedly), it depends on what type of image you created (a regular disk image or a clone image or whatever you did - hopefully one of those two and not a differential or incremental image unless you did those also - then you can restore them as well AFTER you've installed the primary image). The procedures are very clearly documented here:
http://www.laplink.com/documentation/pdf/diskimage/DiskImage_QSG_EN.pdf. I suspect you did a normal image and not a clone image, so the procedure seems fairly straight forward. It does seem like it may take some time (a few hours or more) to complete, but doing it seems like a simple matter of booting to the disk (perhaps creating the disk first if not already done), connecting the external drive, and then following the prompts from the disk to do the restore.
To boot to the CD you may need to change the BIOS to make the CD-drive first in the boot sequence. To do that, wait for the screen that tells you the F key to push to access the boot menu or boot setup. Push it quickly. Make the changes, save your work, and exit. Put the CD in the drive and reboot. When prompted, push any key to boot from the CD.
If you need to boot to a disk because you don't have Laplink installed on the system (which may the case here if you changed operating systems and may be required anyway because the systems are different bit-sizes - that isn't clear from the instructions so I'd use the disk method to be sure), then you can download the ISO to burn the disk from the Laplink site (assuming you don't already have a disk created) but to get there you need to login to your account (and I can't do that as I don't have - or want - your login information).
Laplink - My Account Login Instructions and locations are in the above article.
If I'm reading the guidelines correctly, you can do so with or without the other operating system installed as the image will replace whatever exists if anything exists (and I don't believe it matters if the current OS is 64-bit or 32-bit - it will restore the image by booting to the disk and using the image on your external hard drive though you may not be able to install Laplink on the different bit-size system and get it to restore properly, but since it can be done from the disk and that's what you should do here, that really doesn't matter). You can format first if you wish, but I don't think it is necessary. If you have troubles or run into any issues restoring, you can contact Laplink Technical Support at:
Laplink® Software - Contact Us - Find a Contact (though it may be that you need to login to your account at the above link to gain access to the chat feature or to get the telephone numbers as neither are listed on the page).
I hope this helps. If you run into any problems, contact Laplink Technical support and they should assist you - and better than us because it's their product and they know more about it than we do.
Good luck!