Can somebody win with a blocked pawn?

My rival had only one blocked pawn and I had bishop and pawn, but I lost by time. In real chess, can it be possible?

what more interesting is that if you have a sole knight and the opponent only king and if your opponents time runs out then its a draw but if he has a pawn in addition to the king then he loses.

Yes this is because it is not possible to checkmate someone with a sole knight and king. However, it is possible to checkmate someone by way of a pawn as this pawn can be promoted to a rook or queen which can checkmate the opposing king.

For this exact same reason, it is a draw if the same exact thing happens  with a bishop, as you can`t checkmate with a sole bishop either.

If the pawn can be promoted, OK. But this pawn can't be promoted because it's blocked. My opponent's pawn had a pawn of mine in front of it, so it can't advance, and my king was at the side. That was the final position in the game. I think in real chess I could claim a draw.

"If the pawn can be promoted, OK. But this pawn can't be promoted because it's blocked."

It does not matter. If someone is out of his time, he loses if there is THEORETICALLY way for his opponent to win the game (in your example, it is true that the pawn is blocked, but theoretically there is a chance that it becomes unblocked, and so it can become a queen.) It does not matter whether it is practically impossible (opponent won't help) or not.
And it is a draw, if someone runs out of time, but his opponent could not give a mate, even with the opponent's help.

It is a bit silly rule, but...

there's this fifty move rules that w/o check you can claim draw.  Sometimes I suppose you lose even if the position is theoretically draw but due to time control, for some reason blunder etc.

Depending from the position, time-outs should be draw, even if your opponent has material left, i.e one just one minor piece(this last is most of cases draw, exception of you have a rook pawn, since you could get mated-though not forced).

Now look at this position:

Even if one side wants to lose on purpose, it's impossible to happen. Neither king can penetrate on opponent's position. Then, it should be a draw, and shouldn't be needed even an agreement for settle the draw-this would be categorized as 'Insufficient Material".

I hope i don't missed something obvious here.

The pawn may be blocked, but he could use the king to take the rest of your pieces and then promote it to a queen or a rook.