Susan,
In addition to Eugene's comments, many ham operators belong to local groups such as ARES (Amateur Radio Emergency Services) and/or RACES (Radio Amateur Civil Emergency Service) affiliated with the ARRL (Amateur Radio Relay League).
They (ARES) are all FCC Licensed Amateur Radio volunteers who get activated or deployed in crises large and small, including Kartina. Here's a link to see some of the support offered.
http://www.arrl.org/FandES/field/ares-el/index.html?issue=2005-12-21 For High Frequency (HF) (longer distance) communication, no relays are needed (but a good antenna is needed).
For VHF, natively it is basically line-of-sight, usually ran from a hand-held unit, but you are correct in that there are devices, "repeaters", that collect and re-transmit VHF signals over a wider area (such as a large city or county).
You are also correct that repeaters can be susceptible to disaster conditions, but almost all (at least in my area) are set up with automatic backup power supplies. Also, not all of these are necessarily in populated locations. I know at least one person in my county who host a repeater out of his home. Most that are in places such as downtown areas are high up in building (30 - 40 stories with the antenna on the roof) and would likely continue on emergency power in all but a direct "hit".
Yes, power backup for VHF repeaters would be for limited time but should last several days.
That's when amateurs make a move to HF. For HF, most all amateurs in ARES also have their own individual emergency power kits for their "rigs". We also have a nationwide fun/practice event as a group yearly in a weekend-long event called Field Day, where we compete for amateur contacts world-wide. A key feature of that event is that all stations must operate only on some form of emergency power (battery, portable generator, solar, etc).
Field Days are open to the public and I encourage you and everyone reading this to visit one and hope you will seek out a local Field Day site on Saturday/Sunday, June 26 & 27, 2010. Ask a ton of questions. Geeks like me love to think someone else is interested in our "hobby".
As additional practice we also help with communications for local events (usually the larger ones but small dispersed ones also) such as Charity races, local marathons, etc. We also support communications during large sporting events (100,000 spectators) for other non-profit groups.
When I first started learning about preparedness, this is one of the first organized groups I affiliated myself with, earned my license and started volunteering. Good people!
So, SAT phones were not the only means of communication. But, if by that statement you mean for the general person sitting at home when disaster hit then I’ll agree, that would have been about the only way to get a signal out. Becoming a “ham” does require preparation time, study and testing (though minimal).
One of the primary support activities amateurs provide during emergencies is passing message ”traffic” for individuals cut off (these “Traffic nets” operate daily, regardless of there being an emergency or not). It’s interesting that there are people in rural areas who know their local amateur operators and have long distance traffic passed regularly.
The obvious issue in an emergency is that someone cut-off from others and/or not using public shelters may not have a way pass a message to a disaster support person who could then get it to the amateur operator.
So, if you were not put to sleep by my long answer --
Remember one of the ARRL mottos:
When All Else Falis ... Amateur Radio
P.S. This is why I only have 61 posts, it takes me two hours to write them.