It sounds to me like your keyboard has 2kro or 3kro and needs to be replaced.
There are USB keyboards made which work with a PS/2 adapter. But there is some sort of unwritten rule that these keyboards ship with the adapter in the box.
The USB keyboards that say "This keyboard has 104kro when used with the PS/2 adapter" all feature 6kro when used on USB.
It sounds to me like your keyboard does not currently have 6kro. Therefore adding an adapter won't help you.
When you buy your next keyboard just make sure it has nkro and works with PS/2 and you will have no problems at all and can spend the rest of your life being happy and pwning newbs

There are MANY keyboards from many companies that have NKRO and work on PS/2. But the only kind I actually recommend are the ones from WASDkeyboards.com with Cherry MX Red switches.
But get whatever you like.