I watch the Holmes on Homes show quite abit its a CND home improvement show mainly based out of Ontario. They have done lots of perimter drains and sealing up old basement walls. Its lots of work hand digging around the foundation to the footings. Powerwash the dirt off the wall then start applying the tar,fabric,poly sheeting and this dimpled plastic over top.
As meantioned your going to need to do some exploring which intails drilling some holes or busting some holes into the floor.
You should find out if it is your main sewer pipe leaking if it is then you are contaminating the soil which can be bad news down the road. Also Mould which can make you very very sick can be another problem.
Good Luck
Funny....that's exactly what I actually do (instead of watching it done on TV), yet I rarely dig by hand, that's what the mini-ex is for.
Though I can guess that on occasion, the yards in Toronto wouldn't even allow a mini to do the work. So far, I've been able to get my (39" wide) mini into every yard I've been asked to.
Back to the original issue....go to the three wells near the house, and measure the water level (from ground level). If the level is close to the depth of the basement floor, you know that you are likely dealing with a high water table. Though some will claim that it can be fixed without digging, in reality, either the exterior, interior, or both, needs dug and drained in such a way to lower the volume of water in the ground around the basement.
Digging around the outside, cleaning the wall, and installing the plastic barrier membrane
Membrane
insures that any water traveling sideways through the ground gets stopped, and 'falls' to the drain pipe at the footing. One thing I like about this product, it helps to make up for tough worksites, where it is hard to remove/replace heavy (and poor draining) clay soils with sand or gravel that will readily drain. Though ideally the area adjacent to the wall will be backfilled with a good draining material all the way to the crushed stone surrounding your drain tile. (One thing often not shown in these diagrams, I will use a landscape fabric over the stone bed for the tile, helps keep silt etc out from plugging the tile. Another option would be to use the covered tile.) On difficult wet areas, we have actually backfilled with 3/4" crushed stone to within a foot or so of surface.
Often, if at all possible, I will take this exterior drain tile, and tie it in through the wall, to an interior sump pit. Ideally, inside the basement walls, is a series of tile designed to drain the area under the floor. And yes, you can get water coming up from under a house that doesn't ever reach the perimeter drains.
Only a couple times have I been involved with homes that were cut inside the basement, trenches hand dug, and tile laid throughout. Again, a pump pit (and sump pump) were also added. One advantage with this is the trenches/tile are often lower than if they were installed at time of construction. This helps to get the water levels even lower, giving you a larger margin of water volume to 'monitor' before you have a flood on your hands.
Of course both of these options are costly, somewhat messy, and labour intensive (either yours or the contractors!!) Hopefully you find a somewhat 'easy' fix to the problem you have at hand.