By "tower" I assume you mean the actual computer, right?

If so, mine does this all the time.  The motherboard I've got was one of many
thousands build around 2001 which has defective capacitors on it.  They are
susceptible to being cold.  Whether that literally means temperature, or it
means fully discharged, I'm not sure.  I suspect the later, because here's what
happens.

If I turn the machine on after it's been off for several hours, it often hangs
before even the BIOS initial beep occurs.  Sometimes it'll hang later in the
boot process, but it's usually just plain dead hung upon power up.  If I push
the reset button after that, it boots normally and there are no further
problems.

I suspect it's the "discharge" problem because the time between the power on
hang and my pressing reset is usually less than a minute.  With the exception
of the CPU, not much of anything gets physically warm in that time.  Of course,
if the caps causing the problem are the ones directly adjacent to the CPU,
maybe it is temperature.

If it's off for various periods (say, 30 minutes) it'll usually just boot up.

I'd, briefly, considered replacing the caps, but there's about 50 of them on
the board, some of them are in pretty tight places, and they're all polarized.
The chance of a screw up as compared to having to boot twice in the morning
just isn't worth it.

   - Bill