Launching @ 4Krpm problem .... need tips

[Parmas]

I wish to solve the problem of launching at high rpm. I own a Vitz\Echo hatchback 2001 model and when I launch @ 4krpm from a dead stop its like the left wheel hops and hammers all body of the car (especially the dash). This problem was already there when I was all stock. First I thought I need some good tires so I said until replacement I prevent hard launches.

Now the engine was upgraded to turbo, the gearbox upgraded with LSD and tires upgraded to Toyo 888 series and the problem seems to be on the 2 wheels now!!

I have all things related to suspension still stock... so from where to begin?? Please I am in a budget so don't throw words if you are unsure.

I don't know if it's a problem with my car or the model itself... I am sure that Toyota Starlets haven't that problem.