Vauxhall Corsa problems starting and when driving

my corsa wont start first time, sometimes second and other times im sitting for ages trying and the battery ends up flat, charge battery fully and still no luck, its had a few new sensors put on cant remember which ones, if i get a jumpstart this also happens, also when driving the car will jump, doesnt stall or lose power though, i find that if i push the accelerator down too far this happens, i have been told the car may have a damper, i havent a clue what a damper is, no lights appear on dash, going mad now just typing this, any ideas thanks