I would suggest that the problem lies with your power cord/PSU. The fact that you had this problem before but overcame it by "fiddling with the power cord" tells me that you have either a bad connection or a broken wire. Are you in the habit of winding the cables tightly around the power supply when you pack the laptop away ? We had a salesperson who did that, and I had to cut & resolder the cable on her PSU because the cable between it and the laptop eventually broke down internally due to being bent round too small a radius (about an inch after it emerged from the PSU).
Two things to try...
1) beg steal or borrow another compatible PSU, connect it to your laptop & turn it on. If it works, there's your answer - you need a new PSU.
2) If you can't do 1) (ie you don't know anyone else with the same laptop or a friendly retailer who will let you try), unplug the PSU from the laptop and connect a multimeter across the pins of the plug at the end of the cable (WITHOUT it plugged into the mains !)- do you have a resistance there ? Is it infinite ? If yes, you have a break in your cable.
Hope this helps,