No partitions showing during installation

Solution 1:

You also have the 4 primary partition issue.

My laptop already has 4 primary partitions: how can I install Ubuntu?

Be sure to create recovery DVD(s) first as well as a Windows repair CD.

HP Tools Partition discussion

If you shrink Windows using Windows disk tools and backup HP tools. You can then use gparted to create one large extended partition and have many logical partitions. You can restore HP tools in one if you want. You can make a shared NTFS data partition if you want and you can install Ubuntu in / (root), swap and /home again if you want that as a separate partition.

Update:

If system was an Ultrabook it has Intel SRT which somehow uses RAID. You need to turn off the SRT and then remove the meta-data on both drives. If still booting Windows you can turn SRT back on and it should work.

sudo dmraid -E -r /dev/sda
sudo dmraid -E -r /dev/sdb

Some other issues can be dynamic or LDM partitions if you used Windows to create extra partitions, or left over gpt backup partition table where drive was gpt and you use Windows install in MBR mode.