I have used 2N3906 in place of the BC557 and a 2N3904 in place of the BC547
And it looks like you reversed the mounting, which I think is correct.
in place of the non-polarized 10uf cap I made my own by joining the + leads of 2 x 22uf@50VDC electrotic caps and soldering in the negative leads.
Sounds OK. This design has apparently worked with a polarized cap in both possible orientations as well, so this doesn't seem to be very critical (see some of the discussions in the "simpler single sided serial" forum topics.)
I left the 100uh inductor out.
This however, is bad. To leave this "functionally" out, you should replace it with a plain jumper. Otherwise you have no power to the AVCC pin, which is "not good." I don't know if it immediately explains the problems you are having; partially powered chips behave in all sorts of odd ways!