Did you check the md5hash? that would be the first step for any noob. It's super simple to do an will prevent any unforeseen issues.
Next would be to present us with a picture of your drive partitions. This will be very valuable to all here. You can do this while in puppy or most other distro's or in XP. At this point we don't even know if you can install a linux os untill we see what your partitions look like. Recently I could not install because there was a little storage partition at the end of the drive that would not allow install. So there was no freespace at the end, and that partition had to be removed.
IMO you should not bother with puppy's at this point. Puppy's are awesome, simple and fast, but, in my opinion better for advanced users. Get a distro on the pc and then use/play around with puppy's when you got the basics down, checking hashes, testing a distro Live, posting screenshots etc. With puppy you will have to create "Save File" as you don't want to, and cannot save to much to the CD, the more you save to CD the slower it will boot, each time. You might also run into this issue with the wireless on top of learning how to create Save Files and the intricacies of puppy. If you knew how to do all the stuff above I would say go for it. I hope you like it though, and it works out in your favor.
I am assuming you have Ethernet line for your desktop, you might need this to get wireless on laptop, and, the Ethernet might not work either, you won't know until you try it. You could post the outcome from the directions I gave above but not necessary:
- "From here chose Hardware>Device Manager>click the plus sign on Network Adapters>double click the Network Adapter>chose Details at top>click and copy that info here."