Possibly Dim Witted Question Regarding Comets (Orbits)

One of those things you suddenly think of for the first time in the middle
of the night..

Considering long period comets that have dropped in all the way from the
Oort cloud; how come they don't just plough straight into the sun? Surely
the comets in the cloud are moving very slowly (escape velocity at 1 light
year must be very small) and any such transverse (correct term?) velocity
will be negligible by the time the comet has plunged that far; with all the
time the sun's gravitational pull tugging the comet towards the sun.

So how come they miss?

Sorry if this question strikes anybody as idiotic.

Ian