Having the exact same problem, tried all fixes that I've found on this forum and still no luck, this is kinda ridiculous.
Plesk says this when trying to start named:
ERROR
Unable to make action: Unable to manage service by dnsmng: dnsmng: Service named failed to start
0: /usr/local/psa/admin/htdocs/server/restart_services.php:28 psaerror(string "Unable to make action: Unable to manage service by dnsmng: dnsmng: Service named failed to start")
/var/log/messages has:
Nov 5 22:42:29 EXFAST393 named[30414]: starting BIND 9.2.5 -u named -c /etc/named.conf -u named -t /var/named/run-root
Nov 5 22:42:29 EXFAST393 named[30414]: using 2 CPUs
Nov 5 22:42:29 EXFAST393 named[30414]: loading configuration from '/etc/named.conf'
Nov 5 22:42:29 EXFAST393 named[30414]: listening on IPv4 interface lo, 127.0.0.1#53
Nov 5 22:42:29 EXFAST393 named[30414]: listening on IPv4 interface eth0, xxx#53
Nov 5 22:42:29 EXFAST393 named[30414]: listening on IPv4 interface eth0:1, xxx#53
Nov 5 22:42:29 EXFAST393 named[30414]: listening on IPv4 interface eth0:2, xxx#53
Nov 5 22:42:29 EXFAST393 named[30414]: listening on IPv4 interface eth0:3, xxx#53
Nov 5 22:42:29 EXFAST393 named[30414]: listening on IPv4 interface eth0:4, xxx#53
Nov 5 22:42:29 EXFAST393 named[30414]: command channel listening on 127.0.0.1#953
Nov 5 22:42:29 EXFAST393 named[30414]: could not open entropy source /dev/random: permission denied
Nov 5 22:42:29 EXFAST393 kernel: audit(1131252149.325:0): avc: denied { read } for pid=30416 exe=/usr/sbin/named name=random dev=dm-0 ino=8177079 scontext=root:system_r:named_t tcontext=root

bject_r:named_zone_t tclass=chr_file
Nov 5 22:42:29 EXFAST393 named[30414]: couldn't open pid file '/var/named/run-root/var/named/named.pid': No such file or directory
Nov 5 22:42:29 EXFAST393 named[30414]: exiting (due to early fatal error)
Nov 5 22:42:29 EXFAST393 named: named startup failed
plz help!
