The problem you're facing is called keyboard ghosting.
Typically, ghosting is the result of one or more of following three limitations: the hardware can't read the given key combination, the software on the computer doesn't support multiple simultaneous keys, or the communication protocol between the hardware and software limits the maximum number of simultaneous keys reported. The next section discusses in more detail the hardware design of typical keyboards that limits the number of keys that can be read at the same time.
Since the hardware of your computer worked fine with your previous keyboard, the problem is with your keyboard (unless you can chagen the communication protocol between the two, which I'm unable to do, both remaining options are functionally the same).
The way keyboard buttons are usually wired (for economic reasons) is that they lie on a grid of electrical lines and pressing any key short-circuits a specific intersection in the grid.
So if you have four buttons that each short the following wire couples: [A1][A2][B1][B2] pressing any two will result in your PC noticing the pressure (pressing A1 and then B2? No problem, the events happened at a different time, the PC can distinguish them) but pressing any three or four... well, the last one pressed will add no new connections between the terminals with the numbers and the ones with the letters, so the latest pressure will not be acknowledged.
The buttons that are usually hit at the same time (Ctrl, Shift, Alt, and usually even the WASD keys used for controlling movement in many games) are wired so that their coordinates do not interfere with each other, which is why ghosting only happens for some buttons and not for some others - keep pressing buttons, anyway, and sooner or later you will run into it, on different buttons depending on the specific wiring.
This is why your I button does not work, but your U button does.
What you can do, apart from changing the melee button to a different key that works, is getting an anti-ghost keyboard, which is a keyboard wired in a way that prevents this problem. Be aware that most anti-ghost keyboards do not solve the problem for any and every button combination imaginable: most allow for the contemporary pressure of any 3, or any 4 buttons... which should be OK for this game, maybe not for playing piano on your computer keyboard, which is how I learened about ghosting.