I used EASEUS Partition Manager on Windows.
It had served me well during my previous experience with the HP Mini netbook as detailed here :
I will try to understand what has gone wrong with this and try to rectify with fdisk if possible. Need some time to learn.
1. Is there any need to leave a gap between partitions?
2. That initial logical partition should extend all over the other logical partitions, right?
You can have 4 primary partitions, and one of those can be an extended partition that is a container for logical partitions. The extended partition should extend from its starting sector to the end of the drive, under normal conditions.
With the present 4KB physical sector aware partitioning scheme, the first partition starts on sector 2048 and ends where it ends, there is no space between the end of one primary partition and the next. The following primary partition starts at the next sector after the end of the preceding partition. Within the extended partition, the first logical partition is offset by 2048 sectors from the beginning of the extended partition. Each additional partition will be offset from the end of the preceding partition by another 2048 sectors.
With fdisk, accept the default starting sector for each new partition. Rather than dictate an ending sector, specify a partition size, ie +25G or +100G. Fdisk will round out the size to end on a proper sector boundary. For the next new partition, again accept the default starting sector offered, then continue in like manner for each additional partition.