Could I install ubuntu 10.04 i386 or later on my older computer (amd sempron 2800+, 768 mb ram, 80 GB hard drive)?
Yes you can. I've done this. Simply download the iso for the 32 bits version of ubuntu and install.
I also recommend downloading Ubuntu Server and installing only the things you need. This way you'll get a faster desktop, as Unity requires some RAM to work.