Hi Sinsull, before you go messing with what might be a perfectly fine roof find out the cause. Did it leak when it rained or only when it rains & the wind blows from one direction or when the snow/ice sat on your roof & the outside temp was not high enough to cause any of it to melt. If this is the case you probably in need of more insulation in the attic & vents at your eaves (lower roof edge) & ridge vents (peak of roof) you might also need an ice & water shield which means the removal of 3 ft. of shingles along the eave or against any rising wall (1 1/2 on the roof & 1 1/2 up the wall) where you'd normaly find step flashing. Does the leak run down or within a wall) any structural wall If you'd like to e-mail me (or call, ask & I'll pm my tele#) any info (pictures too if possible) you have I'll help with what I can. Mary feel free to make use of me this has been my trade for 30 yrs.
Barry