I have got the same problem here..
Ive decided to wait till the summer when the grass and weeds are really dry and then im going to incinerate them all with the help of about ten gallons of petrol...This kills all the old roots completely..
In the UK however Id just get a gallon of "roundup" and spray the lot.
Wait a week or so and then dig it all over and flatten out with a rake.
get a few bags of compost and rake in then throw down some grass seed. (not in a heap)
In about 6 weeks your garden will look like Wimbledon center court..Trust me.
