Safari quits when trying to logon to particular sites

Question

After trying to repair the main volume with Disk Utility with no results I did what the system told me. I re-installed from disc 1, finished up with disc 2.
All (except the wire router) settings seemed to be ok. I fixed the router also.
But strangly enough, when trying to log on to Youtube, Safari quits. Also when going to a page of one of my website stores it quits. This is the message that shows up in the error box:
"The application Safar quit unexpectedly after it was reopened.
Mac OS X and other applications are not affected.
Click Try Again to temporarily restore the application's default settings and open it again. Click report to see more details or send a report to Apple."
I've click the Try Again buttom several times but the same thing happens every time.
Every once in a while a message with words to the effect of:
This application's settings are changed, click "..." to temporarily restore defaults settings.
I don't know what to do at this point to solve this. Any help would be greatly appreciated.
Milli.

Answer 1

Since we seem to be embarking on updating in general I'll post my standard post on this.
Updating
Certain steps appear to minimize the risk of an update producing problems.
Number one is to make sure you have a bootable clone backup of your computer in case you do need to back out of it again. This is the only guaranteed way of not having to worry about the results of an update.
Some like to boot from their installer discs or an external backup and verify (and if necessary repair) their internal drives as well as drive permissions. This is done with Disk Utility. You can verify a drive while booted from the same drive but sometimes this produces spurious errors. Repairing a drive (if necessary) has to be done while booted from another disk.
[Resolve startup issues and perform disk maintenance with Disk Utility and fsck|http://docs.info.apple.com/article.html?artnum=106214]
[Using Disk Utility in Mac OS X 10.4.3 or later|http://docs.info.apple.com/article.html?artnum=302672]
[Disk Utility's Repair Disk Permissions|http://docs.info.apple.com/article.html?artnum=25751]
You can also go to the step of booting into safe mode to do the install.
[Mac OS X: Starting up in Safe Mode|http://docs.info.apple.com/article.html?artnum=107393]
[What is Safe Boot, Safe Mode? (Mac OS X)|http://docs.info.apple.com/article.html?artnum=107392]
[Safe Boot takes longer than normal startup|http://docs.info.apple.com/article.html?artnum=107394]
I like to download the update onto my computer and install it from there rather than let Software Update do it. I know a few people who had problems with doing the update via software updater found a manual install to work.
Repair permissions again afterward.
It helps to only install one update at a time and to run the computer for a while to make sure it is behaving well.
The more cautious even like to unplug third party peripherals (see [comment by BDaqua|http://discussions.apple.com/message.jspa?messageID=9040746#9040746]).
Almost all of the above steps (except backup) have been questioned (e.g., [Permissons repair|http://www.macworld.com/article/52220-3/2006/08/repairpermissions.html] as to necessity. Probably many people have done successful updates without doing them. I say they can't hurt, they can very likely do good (especially if your computer isn't regularly maintained), so why not do them to be safe?
[BDaqua's comments on updating problems|http://discussions.apple.com/message.jspa?messageID=8948595#8948595]
[Baby Boomer's comments on updating problems|http://discussions.apple.com/message.jspa?messageID=9025760#9025760]
[Klaus1's post on updating and removing updates|http://discussions.apple.com/message.jspa?messageID=10257902] and [another one|http://discussions.apple.com/message.jspa?messageID=10402175]
For updating Quicktime I'd run Software Update under the Finder Apple and set it to just download the update (since sometimes failed or slow updates seem to result in corrupt drives). After it is downloaded I'd then install it,