For a hard drive that has 4 or 5 partitions, I was able to mount one of them using Ubuntu LiveCD:

sudo mount /dev/sda1 /mnt

but is there a way to mount to the other partitions?

(if using sudo fdisk -l, it only shows /dev/sda)

GParted's snapshot is:

Right now, the fdisk info is as follows:

ubuntu@ubuntu:~$ sudo fdisk -l /dev/sda

Disk /dev/sda: 320.1 GB, 320072933376 bytes
255 heads, 63 sectors/track, 38913 cylinders, total 625142448 sectors
Units = sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disk identifier: 0x1aca8ea5

   Device Boot      Start         End      Blocks   Id  System
/dev/sda1       284993226   350602558    32804666+   7  HPFS/NTFS/exFAT

and then

ubuntu@ubuntu:/mnt$ sudo fdisk -l /dev/sda1

Disk /dev/sda1: 33.6 GB, 33591978496 bytes
255 heads, 63 sectors/track, 4083 cylinders, total 65609333 sectors
Units = sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disk identifier: 0x2052474d

This doesn't look like a partition table
Probably you selected the wrong device.

     Device Boot      Start         End      Blocks   Id  System
/dev/sda1p1   ?     6579571  1924427647   958924038+  70  DiskSecure Multi-Boot
/dev/sda1p2   ?  1953251627  3771827541   909287957+  43  Unknown
/dev/sda1p3   ?   225735265   225735274           5   72  Unknown
/dev/sda1p4      2642411520  2642463409       25945    0  Empty

Partition table entries are not in disk order

Per @lgarzo's request, parted info is:

ubuntu@ubuntu:/mnt$ sudo parted /dev/sda print
Model: ATA ST3320820AS (scsi)
Disk /dev/sda: 320GB
Sector size (logical/physical): 512B/512B
Partition Table: msdos

Number  Start  End    Size    Type     File system  Flags
 1      146GB  180GB  33.6GB  primary  ntfs         boot

The command

sudo mount /dev/sda1p2 /mnt

won't work.