Okay, well thank you all so much for your help, especially you Jhonn, your work on the portable version is Phenomenal and I thank you profusely for everything you have done to help 
Unfortunately it seems I have run flat up against a wall. I have successfully installed the Portable Apps program however the Direct X thingomajig is a bit confusing. I had to download the DirectX End-User Runtimes from the link provided on the Dolphin Portable Apps page, though it appears to be missing a good set of instructions, heh. I have downloaded 'DirectXPortable_9.0c_June_2010.paf' and 'DirectXPortable64_9.0c_June_2010.paf', as the other downloads linked through that page seem to be things like PJ64 and Visual Boy Advance. After that I ran both the .paf's through Portable Apps and it installed on the USB.
Paul suggested to "extract" the dll's out of the Direct X installer, but I got a pitiful amount of content out of the installers that were executed. Here is what was in the USB --> http://imgur.com/a/WSYoD#0 (excuse my terrible drawing skills).
Also, the computer I am using is loaned yes, I have to give it back to the school at the end of next year, with the conclusion of my schooling. In regards to whether my computer can actually run dolphin, it is a HP ProBook 4340s and the specs were the following:
2.3GHz Intel Core i5-2410M processor
3MB level 3 cache
15.6in (1366 x 768) matt display
Windows 7 Professional 64-bit
4GB DDR3-1333MHz RAM
640GB 5400rpm hard disk
AMD Radeon HD 6490M graphics with 1GB VRAM
So not terrible, I think. Anyway, I look forward to people replying!
Unfortunately it seems I have run flat up against a wall. I have successfully installed the Portable Apps program however the Direct X thingomajig is a bit confusing. I had to download the DirectX End-User Runtimes from the link provided on the Dolphin Portable Apps page, though it appears to be missing a good set of instructions, heh. I have downloaded 'DirectXPortable_9.0c_June_2010.paf' and 'DirectXPortable64_9.0c_June_2010.paf', as the other downloads linked through that page seem to be things like PJ64 and Visual Boy Advance. After that I ran both the .paf's through Portable Apps and it installed on the USB.
Paul suggested to "extract" the dll's out of the Direct X installer, but I got a pitiful amount of content out of the installers that were executed. Here is what was in the USB --> http://imgur.com/a/WSYoD#0 (excuse my terrible drawing skills).
Also, the computer I am using is loaned yes, I have to give it back to the school at the end of next year, with the conclusion of my schooling. In regards to whether my computer can actually run dolphin, it is a HP ProBook 4340s and the specs were the following:
2.3GHz Intel Core i5-2410M processor
3MB level 3 cache
15.6in (1366 x 768) matt display
Windows 7 Professional 64-bit
4GB DDR3-1333MHz RAM
640GB 5400rpm hard disk
AMD Radeon HD 6490M graphics with 1GB VRAM
So not terrible, I think. Anyway, I look forward to people replying!