Remember in the old system how if you played enough ranked, your rewards would go down, and no matter what you did, you would win or lose like 11 points per game? Presumably what happens is the same sort of thing, where if you play enough games, the system figures that statistically you deserve to be where you are, so you're going to get very little adjustments to your position for winning or losing. Something about the MMR/confidence (MatchMaking Rating). So old system or new, going anywhere will take a long time.
Actually, it may take even longer with the new system. With the old system, wasn't silver 1250 and gold 1500? Let's even be generous and say you needed 300 elo to get from silver to gold. Now if I'm not greatly mistaken, the minimum elo change once you'd played like 200 ranked games in season 2 was +/- 11. So for 300, let's round up and say 28 straight wins.
With the new system, starting at silver V and going to gold I, if what you describe turns out to be a general rule and you get +/- 11 LP for each game, you would need 10 straight wins for each of the 5 tiers (possibly 1-3 extra when you near the top of silver I since the game ramps your reward down there to make sure you're not on a streak or whatever). In addition, assuming you never lose, you would need 2 promotion game victories for the first four tiers, and 3 (I think, someone correct me if I'm wrong) for the final upgrade 3/5 promotion match. So, (5*10) + (2*4 + 3) = 61.
So, season 3 is supposed to give you a better feeling of making progress, but it sounds like you're stuck with winning roughly 60 straight instead of 30 straight, for DOUBLE the number of hours you would have previously had to put into the game, to go from silver to gold.
Scy or other math people, if there are hard numbers that prove otherwise by all means post them, these are based on what Terbinator posted and what my S2 experience was.