I upgraded two workstations from 12.3 to 13.1 without a problem. The third workstation upgrade has not gotten very far.
During the initial phase of discovering hardware and software, it pauses a rather long time on “Probe hard disks” then hangs forever on “Searching for Linux partitions.” Obviously there are fully functional linux partitions since the computer boots just fine to v12.3.
I have had this before. The first thing is use a utility like gparted to make sure all partitions are good. Windows partitions can be bad if they exit. If there is more than one hard drive, you can disconnect any not needed for the new install. But it is a guess as to why the install takes so long and not normal.
How am I to know that you are not dual booting. Note I said IF Win8 it could be a problem if not shut down correctly and MIGHT cause the hang you are seeing. If Windows is not involved then it is something else. Maybe run fsck on exiting Linux partitions.