One correction...it almost sounded like a loud knocking, not a tick.  I
drove it the day before and it was A-OK, and just came out of the blue right
away when I started the car up today.

first things first! have you checked the oil level? if it's not got
enough (or the wrong grade oil) they will be starved of oil and tick.

all the 944 engine use hydraulic tappets (lifters) and so they
constantly adjust themselves. there's no need (and indeed no way) for
you to adjust them. moving to a thicker oil wouldn't help either (in
fact it would make things a LOT WORSE). if they are blocked the best
way to fix them is to replace them. they are reasonably inexpensive
and not too difficult to change. if you don't mind using such things
you could try a good engine flush to try to remove some of the sludge
from your engine and increase oil circulation, this may bring them
back to life.

the ticking noise you hear my also be an injector about to fail.
injectors usually make a ticking noise all the time once they go, so
it's failure may be immanant.

if the ticking noise only happens from cold and goes away after about
5 to 10 seconds or raising the rev's to about 2000 rpm, then it's most
likely the hydralic tappets. if you don't mind this nose, then there's
no reason to change them.

hth,
jules
'89 944 turbo se
'83 924 lux