Replacing the hard-drive when it's broken is certainly a real possibility. Any laptop hard-drive will fit, and they're easy and cheap to get by.
Careful: there are two, incompatible flavours of hard drives: the older parallel ATA (PATA) and the newer serial ATA (SATA). Make sure you get the right sort for your laptop. From the looks of your screen shots, it appears to me that you have the older PATA hardware (in which case you won't find anything S-ATA anywhere in the BIOS settings).
I missed that this is a laptop, so my advice about cleaning it doesn't apply - at least not in the same way.
I'd check into the second thing RayG found first of all, though; that sounds pretty close to what you're describing.
On the issue of cleaning: Laptops, actually, are even more prone to overheating than desktop systems, since they have a much more restricted path for air cooling.
However, from the screenshots you've posted, it does appear that this may be a hard drive failure, although it still could be overheating.
Can the problem occur when the laptop is cold (i.e. when it's been sitting turned off for a long time - at least an hour)? If not, how warm is the laptop?
If it does occur when the laptop is cold, then, as other posters have suggested, try running using a "live CD" or DVD (that's a complete Linux O/S you download and burn to a CD or DVD). If it does not hang then, then you can be pretty sure it's a hard drive problem.
If it doesn't occur when the laptop is cold, then take a can of compressed air and blow through the laptop's cooling vents. This may dislodge some of the cruft that is likely to have accumulated. In my case, if I do not periodically clean my laptop's vents, the machine will eventually start overheating (although it shuts down, rather than hanging). (I actually use a vacuum on my laptop, but that may be sufficiently powerful to damage the machine - it's not recommended, from what I understand.)
If it appears to be the hard drive, as mentioned that's fairly easy to replace. You can also get an external USB case to put the old hard drive in; that would allow you to copy any data you have saved on the hard drive (although you should do a backup to CD/DVD or other computer first, since Murphy's Law applies).
Note that if it does hang when running from a live CD, it may be that the whole machine is dying; you can try taking it to a shop to get diagnosed, but a) it's hard to find good repair stores and b) they may not understand Linux anyway.
Anyway, good luck.
ETA: If you do get a new hard drive, also make sure it's a
laptop hard drive (2.5"). Desktop hard drives are physically bigger (3.5") and won't fit.