I recently got a Nikon D3100 and, after trying it out, I went to upload the photos to my laptop. In doing so it asked me to download Nikon's version of Windows Photo Gallery, but now I am not able to view my photos. Is there anything I can do to resolve this?
It sounds like you were shooting RAW images. These types of files are not directly viewable without special software that understands how your camera works and how to interpret the data from the sensor. They offer a lot of strengths over JPEG, such as being able to adjust white balance and recover from some over or under-exposure much more easily, however the cost is that you need to use the special software to read them, finish your post production and then export to JPEG or similar image formats so that they can be read on other computers.
You need to actually use the software you installed to view them. You should be able to launch ViewNX or you can try a third party tool such as DarkTable to work with the images. You can find more information on the benefits of RAW files here.
As Stan Rogers pointed out, there are also tools available to allow explorer to view thumbnails of the images, but it sounds like you don't have any of those currently installed.
Is there anything i can do to resolve this?
Perhaps downloading a free photo manager/organizer/viewer would help?
I would recommend XnView MP if you're on the cutting edge or XnView Classic if you're more conservative.
Install & run it (don't forget to associate the image files - it is easy, the program asks for this).