There seems to be a small play between my whole fork/headset/stem. When I lift bike, I can feel fork move just little bit and a slight movement on bottom spacer of the tube. I tried tightening the the stem bolt on the top and sides while pressing it down as hard as possible but it still doesn't work.

You probably should try out LBS. Besides, if you indeed busted your headset, I am pretty sure you don't have (or you don't want to buy) the set of tools to replace it anyway. (If you are mechanics and do have tools, you won't be posting this question, right?)

First of all, you need to get it adjusted pronto or you're going to ruin your frame. Fortunately, it's easy to do with just a 5mm allen wrench.

1. Loosen the bolts that hold your stem to the steerer tube. It needs to be able to slide.
2. Now tighten your top cap bolt. It needs to ge tight enough that you don't have any front-to-back play but loose enough that your front wheel can flop side-to-side.
3. Retighten the stem bolts.

Or - your top cap may be making contact with the top of your steerer tube, making it impossible for you to tighten it down as much as you need to. If this is the case, take one of the smallest spacers out from beneath your stem and place it on top. Reinstall your top cap, tighten properly, then tighten your stem bolts.

How is that going to change anything? If there are an insufficient number of spacers to locate the cap above the steerer, then moving spacers around isn't going to change anything. Think about it. Anyway, in a situation like this, my advice would be to take it to a competent LBS to determine the proper action that is needed.

Edit: Moving this thread to Bicycle Mechanics Forum.

You're right. Dude would need to place an additional small spacer above his stem to correct it making contact with the steerer.

Ugh...I shouldn't post pre-coffee.

https://www.parktool.com/repair/readhowto.asp?id=65

This.

I had a similar problem once and realised it was just because my top cap was pressing on the steer tube and not on the stem/stack of spacers. Make sure your stem or a spacer above your stem acutally protrudes above the steer tube before you tighten everything down. Then make sure the fork doesn't seize up as a result. If it does, then you need a few shim spacers above the lower crown race to make sure your fork isn't jamming against the head tube. Once you've got clearance below the head tube, and everything is pressed down appropriately above it, you're good to go.

Yeah...I don't know what the hell I was thinking when I told him to just move his spacers around. My brain functions about as well as Ozzy Osbourne's first thing in the morning.

If you need to replace it, you can build your own headset removal/install tools for CHEAP. A copper pipe for the removal tool and a bolt and nuts/washers for the installation tool.
A few minutes on the interwebs and you can find the instructions.

Scrod works in a LBS. Your statement is either contradictory, or an insult to Scrod. *evil grin*

I totally deserve the insult. I clearly wasn't thinking clearly. Uh...what?

You know, the thing doesn't suck just because you don't know how to adjust it. It's not that diffiult, but from what you wrote, I don't thhink you know how to. Either read how to do it on Parktool website, or have your LBS do it. IT's easy and quick. That's what the design is good for. (there are things it's not good for, but adjustment isn't one of them).