Some possible fixes:
1. Are you SURE your SD card is 2 GB? Sometimes they are mislabeled, and you might actually be using a larger SD card. PNY is notorious for that. Check that by popping it in your computer and going to Preferences or Settings or Get Info or whatever.
2. Is the SD card locked? There's a little slider on the side. You want it to be unlocked, or the data will be inaccessible.
3. Do you have the proper version of PM downloaded?
4. Have you tried these SD cards in a different Wii? There might be something wrong with your Wii SD card slot (rare, and tragic, but a possibility).
5. Have you ever had PM working on this Wii before? Not really a fix, but it helps isolate the problem
My answers to your questions:
1.Positive. While reformatting, I saw it had 1.89 GB of storage space.
2.The SD card is not locked. I had it running on a laptop which means it is not locked.
3.I have 3.5 nohomebrew version.
4.None of my neighbors have a Wii and the people that I know have one lives quite far away from me. Also, my Wii is an ancient relic of the past as it is a second-hand one and the previous owners did not take care of it at all (Broken nunchucks, broken disk slot, an abundance of freaking Miis, crappy shovelware games, lack of internet connection, and my parents were not aware that it is a used Wii)
5. As stated, I am still trying to see if I can mod my Brawl.
Thanks anyways. At least you tried to help.