Hi there and welcome !
Sorry for the delay in replying, still catching up after the Christmas Holidays...
The "checksum invalid" would normally refer to the disk image...
The easiest way would be for one of your friends to download the update and burn to CD on a Mac, it can be done with something like Nero on a PC but you would have to make sure that the CD was HFS not ISO, but as you've already tried this...
I presume you have been downloading the update from here...
http://docs.info.apple.com/article.html?artnum=75103
In theory it should just be a matter of installing OS 9.04 and then applying the 9.1 update...I must admit it has been quite some time since I have done it myself !
Have you got any further ? I'll double check my database's to see if I can find anything that may help.
The only thing I can think of at the minute, is to try booting of the install CD and then applying the update, or have you already tried that ?
regards
Ric