HI - What method did you end up using? I'm looking for similar information myself. Many thanks...

If you don't want to drill holes, use a powder-actuated nail driver. This uses a .22 caliber load to drive the nail through the board into the concrete. Lowes sells the Remington braand for about $25. You load the nail, insert the sheel, and hit with a hammer. Works great! Put one every couple of feet.

I wouldn't trust construction adhesive alone.

Reading between the lines, I take it you want to fasten the 2x4's to the concrete and then nail or screw the deck boards to the 2x4's? If so, why don't you let the deck float on top of the concrete with only minimal fastening on the perimiter to prevent movement. If you are dead set on fastening all the 2x4's to the concrete, I would use the power nailer as suggested in 2 or three points per 2x4 and supliment with a waterproof construction adhesive such as PL400