It could be because you got punished during the season. That would mean you haven't got any of the rewards. This has to be an actual punishment (I think the only actual punishment is a temporary or permanent ban), so only getting a warning shouldn't be the case. It only counts punishments from the current season+preseason, so if you got punished in preseason 2015 you would also lose your 5th season rewards, but it wouldn't affect your season 6 rewards (unless you get punished again).
If you got the icon but not the border it's because you got to silver in one queue (ranked teams or ranked solo/duo) which means you get the border in normals/arams and wherever you placed silver, but not on the other queue. I don't know how this works with dynamic queue, so it could be that.
The last option is that you got to silver in ranked teams but you didn't win 10 games. You had to WIN at least 10 games with your team to get the rewards, otherwise you get nothing :/
Now if any of the above are the case you should contact support (search "support league of legends" in google, I'm from my cellphone so it'd be a pain to look it up) and submit a ticket.
It could be because you reached that elo after the official ranked season had ended but the preseason was going and ranked was still up. Just a thought
If you got the icon but not the border it's because you got to silver in one queue (ranked teams or ranked solo/duo) which means you get the border in normals/arams and wherever you placed silver, but not on the other queue. I don't know how this works with dynamic queue, so it could be that.
The last option is that you got to silver in ranked teams but you didn't win 10 games. You had to WIN at least 10 games with your team to get the rewards, otherwise you get nothing :/
Now if any of the above are the case you should contact support (search "support league of legends" in google, I'm from my cellphone so it'd be a pain to look it up) and submit a ticket.