Why won't mobs spawn in my trap

I've built a mob spawning trap but mobs are not spawning.

It's a tower that is 10 blocks long x 5 blocks deep x 35 blocks high. At the top of the tower (33 blocks) is a spawn floor. The spawn floor is 10 blocks long x 3 blocks wide. There are signs on the edges of the spawn floor.

I've used a mapper to find all the caves in the immediate area and they are all lit.

When I'm standing on the ground (35 blks below the spawn floor) nothing will spawn.

The game is set on normal, single player, and mobs will at night on the ground, just never in my trap.

Here is a pic of spawn floor (torch added for pic, it is completely dark normally)

Here is a pic of the whole structure (tower is built in the cliff).

I'm not sure what I am doing wrong. Please help.

There are two points to remember that may seem contradictory: first, like Nicholas pointed out, you need to makes sure that your mobspawner is the only nonlit space in a pretty big area around you (I think the area's actually about 150x150 blocks), but second, you need a lot of empty space around. In other words, minecraft will choose places that have a lot of surface area (not volume) to spawn mobs in, so if you were to have a lot of open caves beneath your mobspawner, the game will flag that area as more likely to spawn mobs in. You just also have to make sure that it's all well-lit, then you've effectively tricked the game into flagging that area to spawn mobs in, but then conveniently your mobspawner is the only dark area where it can do so.

I would recommend you take a look at this tutorial. You may not want that particular style of mobspawner, but it goes over the prerequisites of any good mobspawner quite nicely.

I think the main problem here would be other places where mobs can spawn. Yes, you said you lit all the caves in the "immediate area", but about how large is that area? If I recall correctly, mobs can spawn in a 128x128 size box around the player. Most of these will immediately despawn due to being too far away from you, but it will still take away from the spawning rate inside the trap, which doesn't have that large of a spawning area. I recall from experience having a 30x30 sized mob trap (Which has a spawning area 30 times bigger) with a fairly low spawning rate for mobs. Your best bet is probably to enlarge the spawn area a LOT. With such a small spawn floor, even if you missed just a single cave, that would take out a HUGE (Probably over 90%) chunk of your mob spawns.

By the way, don't worry if even after enlarging the spawn floor and lighting up all the caves your mob trap doesn't work at night. Unless you've lit up a TON of area (A 128x128 area is equal to 16384 squares, and at a generous estimate of 64 squares per torch, you'd still need 256 torches to light it all up) around the trap, a lot more mobs will spawn outside of it than in the trap, and there's not much you can do about it except use a bed.