It's not too hard to get diagnostic information on the hardware. I'm going to give you some command line instructions which should work on most any Linux distribution, however you might need to download some utilities (if you won't have internet access, consider storing some packages on a live flash drive you could use).
First thing I'd check is that the hard drive isn't reporting any issues. Most hard drives support SMART to report issues, which you can check with the following:
sudo smartctl -d ata -H /dev/sda
This should give something like
=== START OF READ SMART DATA SECTION ===
SMART overall-health self-assessment test result: PASSED
if everything is okay. Smartctl is probably installed on your live distribution by default, but it wouldn't hurt to check. Quick explanation of the options: -d is the disk type, will probably be ata, and -H is the drive - it'll differ based on the type of drive and might also be /dev/hda. Note that smartctl is not a perfect measure of hard drive performance and you are likely at a higher risk of a failing hard drive if you purchase a used one.
After that you can get some generic information about hardware. For this I'd recommend lshw - that probably won't be installed by default. Just execute the command without arguments like
and you'll get detailed information about all the hardware on the machine. I recommend doing so in a full screen terminal. Pay special attention to the *-memory section to make sure it has as much as it says. You can also use
for a more compact list of internal hardware.
You might also want to check how the battery is doing. This is simple enough with the acpi command, which some distributions include by default but is another thing you'll want to double check. To see the battery's design capacity and percentage of that type
You'll notice a percentage on the end of the second line, this is the current maximum capacity of the battery compared to the designed capacity (they degrade over time, you can usually expect 98-99% for a new one). If you've got low percentages there you can expect minimal battery life and will likely need to replace it if you mean to use it on battery.
If something is going to be in immediate, obvious trouble it's probably the hard drive. RAM is something else to watch out for.
That's all I can think of off the top of my head, might add more later.