Occasionally my PS3 refuses to sign in.? After trawling through a billion pages I finally found the solution.
Change your DNS servers to 126.96.36.199 or/and 188.8.131.52
All the other settings don’t really make any difference.? My router was even set up to put the PS3 in DMZ (Demilitarised Zone) which didn’t help at all. ? The fault really lies with your ISP, apparently.? My original DNS was 184.108.40.206 and 220.127.116.11.
Thanks to amstel78 from the PSN forums.