Yes, I can see ROM version, initial screen with floppy disc, so ROM is attached properly. It is something else?! I really don't know. Power supply is ATX 350W and caps are "fine" (soon I will try with new one).

Have you tried it again without the new ROM socket 'risers'? If it works without the risers then perhaps the pins on your riser sockets are too thin (or flat, where round would likely work). The reason this springs to mind is that my FastATA had round pins IIRC, which would surely stretch the contacts on the Amiga's ROM socket, whereby inserting flat pinned ROMS would likely not work now due to the original ROM socket contacts being strained. I can't remember for sure as it was 9 years ago that I built that setup of mine, but it's worth considering if all else fails. I haven't touched it since I built it and it's worked fine for me all these years. I can't quite remember whether I used risers or not, could of been the risers with thick round pins...but anyway, worth a look I think.
Without any drivers, the FastATA should function exactly the same as the standard A1200 IDE port (assuming you're using the first IDE port I assume). So your hard drive should show up in the 'Amiga Early Startup Control' boot menu.
Maybe you're floppy drive is acting up anyway being as though you mentioned it in your first post, we don't know for sure yet whether it is related to your FastATA issue.