Too bad about that meter since 0.2 could still be acceptable but 0.4 is not. The way F3 is supposed to work is to either let the current through (without much voltage drop hopefully, hence the low resistance) or pretty much not let it at all when tripped.
It's one of two options:
1) Your F3 is faulty and has too high resistance that causes it drop too much voltage (but not trip). This drop is of course converted into waste heat as power is dissipated.
2) The Pi is fried and has internal short-circuit somewhere, but not big enough for the polyfuse to trip (again, maybe because it's faulty).
If it's 1 then just desolder F3, or just solder a piece of wire on top of it to short it permanently. This will fix the problem at the cost of not having a fuse anymore but I suppose you wouldn't be asking here if you had a replacement
Now, if it's 2 and you do that, the Pi will most likely end up smoking but then again if it's already fried so what. It's not working now anyway.
Fell free to get a second opinion though
Oh, and you can try by-passing F3 for a short time without soldering, just cover it with a wire or tinfoil and clip it with something.