Somewhat OT - can underpowered power supplies damage a system?

[Thomas Cameron]

Say, hypothetically, I have 8 identical Intel DG45ID motherboard-based 
system with 8GB memory and a single drive with a cheap-o generic 300w 
power supply.  All running Linux, so sorta on-topic.

Say those systems have been running for over a year, but lately they've 
been really flaky.  Random lockups, sometimes they boot with garbage 
characters on the screen instead of the normal OS boot, sometimes they 
hang at various parts of the boot sequence, spontaneous reboots when 
kickstarting.

Say the Antec web site says I need more like a 350w power supply, and I 
read somewhere that PSUs tend to age and get less efficient over time, 
so I am guessing that I've been starving these things for juice for 
weeks or maybe months.

Hypothetically, could I have actually damaged these systems if the PSU 
was under-powered?  Or would a new, higher powered PSU fix the problems 
I've seen?

I would guess that too much juice might hurt the systems, but would too 
little actually damage anything?

I know it's not thermal, they're in a very cold room with dedicated HVAC 
and the airflow is great.

Hoping someone who knows more about electronics can chime in.

Thanks
Thomas