Here is what I posted on the other thread.
I don't know what kind of uke you have, but it sounds like the nut will need to be replaced. The only way the note can sound the same at the first fret and open is if the string is sitting too low in the nut and the string is actually resting on the first fret in the open position. You need to make sure that there is a space under the string and the first fret when it is in the open position. Check it out and report back.
In addition, if two strings play fine, then the nut slot is too deep for the G and A strings and the strings are resting on the first fret. You need a new nut. Take it to a luthier and have it done right.