I doubt it's anything less localised than a fault of the computer you're using. It could be a DNS problem but I doubt that, since you're able to view some Youtube videos.
Try this anyway:
- Press Window+R.
- Run "ncpa.cpl".
- Right click Local Area Connection (or Wireless Network Connection if you're using wireless) and go to properties.
- Double click Internet Protocol TCP/IP. If you're on Vista you need to select the ipv4 one.
- Make sure the dot is in "Use the following DNS servers" or whatever it says. The bottom bit.
- Put these IP addresses in for primary and secondary, respectively: <b>208.67.222.222</b> and <b>208.67.220.220</b>.
- Press ok until you're out of all of the dialogs.
- Try to view some Photobucket pictures.
- ???
- Profit.
Can you try another computer on the same internet connection?