HP notebook/latptop generally do have a built in function in BIOS to make a short test of the hard disk, not sure about your specific model, but you can check.
About bad blocks, assuming the disk is a relatively recent model, your best option is to perform a S.M.A.R.T. test, which is much much faster than a scanning for badblocks.
I'm not sure that scanning for badblocks make any sense these days, because SATA disks are designed to automatically replace bad sectors (using some spare storage on the same disk) when some error occurs. Once the spare blocks are exhausted your best choice is to replace the hard disk.
Anyway, to check the disk using S.M.A.R.T. technology you need the command smarctl, provided by the packaged smartmontools, available in repo non available on a brand new PCLinuxOS ISO image:
gmsartcontrol is a graphics interface to smartctl, your best option is to install both packages, available there are a general healt status, a short test (2 minutes) a long test (1 or more hours), please note that SMART status is based on data collected along the whole life of the hard disk, not only data collected at test time.
from command line:
smartctl -H /dev/sdX (general healt status)
smartctl -t short /dev/sdX (perform a short test)
smartctl -t long /dev/sdx (perform a long test)
smartctl -l selfest (list and status about already performed tests)
if you want to perform a scan for bad blocks, the command is badblocks, is available on the official live ISOs, and can be used directly from command line, see man badblocks for further details:
or you can use fsck on ext2/3/4 partitions (that in turn will call badblocks):
fsck -f -c /dev/sdaX (read-only test)
fsck -f -c -c /dev/sdaX (read-write test)