Hi Jacem5. I have more controllers than you can shake a control stick at. I will question the quality of your controller first. Generic controllers are about as good as street corner hot dogs. They both look good at first glance but don't do you any good in the long run. I searched for Power Pad and came up with too many results which says to me, "Generic".
I have almost all Logitech controllers. MOMO racing Force feedback pro, Wingman force 3D, G15 and G5 gaming keyboard and mouse. I also use USB adapters to connect genuine PSx and N64 controllers. All of that cost me mucho mula. I assume your not looking to make an investment though so I'll try to help with this controller but keep in mind, if the game works without the controller then it's not the game that doesn't work. Eliminate the obvious.
You need to know if your OS see's your controller. What OS are you running. If it's windows, ( the only one I can help with) go to control panel/game controllers. It should be listed there if it's plugged in. If not, it may not be compatible. You can click on the ADD button and find a description that yours fits and try that but no guarantees.
Most games make controllers selectable. If I could offer some personal advice though, don't use a controller for FPS games on a PC. KB & Mouse is far superior. Just my opinion though. Different strokes for different folks but if you end up on the wrong end of my M4A1 I'll prove my point. LOL
As far as the jet ski games you mentioned I can only think of a couple but they don't fit the profile exactly. Wave Race was a good one on Nintendo 64. PS1 had Jet Moto. Neither on lets you upgrade as far as I remember. If you like older console games, try googling "emulator". They are a little tricky to get running sometimes but if you are patient and follow advice, they are really satisfying. You can find a few forums that will help. Be aware there are some legal issues you need to know about to keep you on the right side of the law. A reputable EMU forum at this link.
I have more I could add but it's supper time and does it smell good! Feel free to ask any more questions you have and we'll try to get you an answer and get you gaming.