Is this blocked situation a draw? If not, how can I win as Black? I had a game on chess.com that ended in a draw by agreement. Is this a real draw? If not, what are my best moves as Black? 

Computer analysis on chess.com suggested this continuation, “39. Qe2 Rf7 40. Nf3 Qc7 41. Ra2 Bf8 42. Qc2 Rd8,” saying that "Black has a moderate advantage".

[FEN ""]
[Event "Live Chess"]
[Site "Chess.com"]
[Date "2015.05.06"]
[White "fianwhatto"]
[Black "bigother"]
[Result "1/2-1/2"]
[WhiteElo "1432"]
[BlackElo "1400"]
[TimeControl "10|0"]
[Termination "Game drawn by agreement"]
[WhiteToggles "0%"]
[BlackToggles "0%"]
[startply "77"]

1.c4 d6 2.Nc3 e5 3.Nf3 g6 4.e3 Bg7 5.Be2 b6 6.O-O Bb7 7.d3 Nf6 8.e4 Nc6 9.h3 O-O 10.a3 Nd4
 11.Bg5 Qd7 12.Nxd4 exd4 13.Nb5 c5 14.a4 a6 15.Na3 h6 16.Bh4 g5 17.Bg3 Rfe8 18.f4 Nh7 19.f5 f6 20.Bh5 Re7
 21.Bf3 Bc6 22.b3 b5 23.a5 b4 24.Nb1 Qd8 25.Nd2 Qd7 26.Bg4 Qd8 27.Bh2 Qc7 28.g3 Nf8 29.h4 Nd7 30.h5 Ne5
 31.Be2 Qb7 32.g4 Rd7 33.Bxe5 dxe5 34.Bf3 Re7 35.Qe2 Qc7 36.Qf2 Qb7 37.Rfe1 Qc7 38.Bg2 Qb7 39.Qe2 1/2-1/2
This is a dead draw.

There are no sensible piece sacrifices for either side. 

There is no plan that isn't easily parried (Black could gang up on the a5-pawn with Qd8 and Bc7, but white just doubles the rooks on a1 and a2. White could try to invade with the knight to b6 and d5, but black would just go Bxa4 when the knight turns up on a4.)

Black isn't better here and black isn't worse. There is just nothing any side can do. 

Edit: I think I'll expand on this a bit, because for some reason the concept of a dead draw seems to be hard to grasp. 

Positions are usually evaluated based on best play by both sides. That can be tricky because there are positions that should be equal or even favourable for one side, but in practice are more promising for the other side. 

But in the given position the level of play needed to hold a draw against best play, is very, very low. To put it differently: A 1500 player would have no trouble holding this position with white against Magnus Carlsen. The fact that a computer engine gives a small plus for black doesn't mean black has any advantage whatsoever. It just means that engines aren't yet able to understand completely blocked positions and other kinds of fortresses very well.

Let's go back to our fictional 1500 player. The only thing he has to do is keep e4 and a5 well protected and there is nothing Magnus Carlsen will ever be able to do. Now e4 is already over-over-overprotected. Let's say Carlsen comes up with the cunning plan to attack a5 via Qd8 and Bc7 and our 1500 player isn't sharp enough to double the rooks quickly. Now the a5 pawn falls …

r2q2k1/r7/p1b2p1p/b1p1pPpP/1pPpP1P1/1P1P4/R2NB3/1R1Q2K1 w - - 0 1

1.Rba1 Bc7 2.Ra4 Bxa4 3.Rxa4


Black is a pawn and the exchange up. Possibly the computer will give a even better score for black, but the facts haven't changed: This is still A DEAD DRAW.