I have tried frying salmon filet and besides the fact it was very raw on the inside it fell apart when I tried to flip it over. Why?  *Skin was on. 
Ok so you said salmon fillet. So my first question is how big is the filet. Fish don't develop protein chains to hold together the same way red meat has. So the flakes don't really hold together if pulled too hard, so I wonder if your fillets are too big. When I cook fish, especially salmon I try cut the fillet into serving sizes portions, maybe 2 inches across (assuming a full sized fish here). This helps keep the fish to a manageable size.  There is also a tool that is very aptly named because it was designed for this use and it's called a fish turner. This is a thin and springy or turner that would better with fish because when scooping up the fish it doesn't force the fish to reshape itself to the more rigid spatula and therefore you get less fish breaking apart.  Do not turn the fish too many times. Leave it on one side and let it do all the cooking on that side that it needs, flip it once and let it finish.  This will produce a nice crusty finish. As far as getting it to cook through the center, well that takes patience. Cook on a medium low heat but cook it for longer, like 8 minutes on each side (experiment, don't rely on my telling you 8 minutes). Then when you take the fish off the pan, put it on the plate and let it rest for a few more minutes. The fish will still be cooking on the inside and will finish up if you don't serve it too early, but of course don't wait so long that the fish cools. You want to serve it while it's still hot, but not scalding hot. 