Everything looks normal (well, normal for NLW) at the time of writing
(1745GMT 09 Feb 2016). There may well have been some earlier outage.
One problem may be that for PC browsers (I don't know about tablets), there
are more "tiles" (the pictures with links) than there are spaces available
on the home page.
When I open the web page, I only see 6 "tiles" (2 rows of 3). There are
actually at least 11 (some may be transient and for limited periods):
Welsh Newspapers Online
It appears to be pot-luck as to which 6 you get.
Try refreshing the browser screen and see what happens. Sooner or later the
one you really want appears.
"New Catalogue" (if it appears) has a link to other things.
This is probably a "design feature".