What kind of grass, do you know? If it's nutgrass or Bermuda you have a tough chore in front of you. When using cardboard or newspaper, it needs to be laid down where there are not any cracks and in a thick layer. I use my cow feed sacks and layer them 4-6 deep at least and make sure there is lots of overlap at the edges and then cover it all with a solid layer of mulch. It works on nearly everything, but Bermuda will find it way up through it and it doesn't deter the wild onion at all as far as I can tell. I guess their growing point in the spring just pierces through all of the layers. I would expect nutgrass to be a lot like the onion. Bermuda roots can just live a long time under the layers and wait for enough decomposition to occur and then they'll surface again.
You might try again with a thicker layer of cardboard - no cracks or seams. Otherwise options may be to dig out and replace the soil or use a herbicide and see if you can kill everything, but even that's going to be hard if it's Bermuda or nutgrass.
