Overkill on tags...

Described problem is not lag, or connected to lag in any way. Two java tags first on list "java" last on list "Java" . What is "space" tag for? also "help"...

Some things you should provide:
Amount of tiles being drawn.
Amount of FPS without tiles being drawn.

Amount of FPS with tiles being drawn.

2734 tiles being drawn

Are 2,734 tiles really all on screen at the same time?

If not, your first step is to calculate which tiles are on screen, and draw only those tiles...

If not, your first step is to calculate which tiles are on screen, and draw only those tiles...

I think that's what the giant if statement is trying to do.

One way to test if you're properly culling the non-visible images is to throw in a debug "drawcall count" printout at the end of the frame. Just reset the variable to 0 at the beginning of every frame, and increment it inside the culling branch (i.e. right after the "draw" call).

Some kind of scene-graph or space-partitioning tree might make your draw calls more efficient by keeping you from looping through every tile every frame, but at <3000 tiles total, that still shouldn't be a costly loop. Methinks there's more going on here. How expensive/heavy is a draw call in slick2D?

Edit: fairly expensive, apparently. Check out this link for some suggestions. Biggest one is to turn your tiles into sprites packed into the same spritesheet and use the DrawEmbedded call instead of just Draw.

All I know is what I see in your code and what I read on that link: image.draw is a heavy, costly method compared to image.drawembedded. Did you read the suggestions? From the wiki:

Even if you aren't using texture atlases, you should still use drawEmbedded whenever possible. Calling Image.draw
requires various matrix transforms, plus it sends the quad to the GPU
with glBegin/glEnd. Ideally, you should be minimizing calls to
glBegin/glEnd by using startUse/endUse whenever possible.