I doubt it's a memory issue. First thing you should do if it's locking up is boot with safe mode, & see if you can replicate the issue. If you can't (& you most likely won't) then that tells you it's something that only runs in regular mode. This says you have a piece of software that is eating up resources, or doing something it shouldn't.
I would assume it's something malicious, those programs like to eat resources like it's a digital buffet. Download ccleaner, & run through your startup list (or just use msconfig). Research anything you don't know what it is, & get rid of anything not required to run the OS, or some functionality of the laptop.
If you take it somewhere, they are likely just going to charge you to wipe it clean & a do a restore to factory defaults.
Sorry, I do that anytime I see a suggestion to take a laptop apart. Now for the answer...
ASUS laptops (and a good chunk of laptops I've seen in general) have issues moving air to cool its innards.
I've been using an ASUS one for over a year now and mine did the same thing. I picked up one of those $20 coolers that sit under the system (got it at Best Buy even) and started keeping the cooler under the laptop all the time.
No more problems.
The air on them tends to get pulled from under the laptop and sitting it directly on your lap or on a table restricts that airflow. Eventually the system will overheat and shutdown. I don't have my cooler plugged into my laptop a vast majority of the time, just the added height gives it the room to move more air around. If you get into a graphically intense game, then plug the cooler in to assist with increasing the airflow even more.
This solution will help with MOST laptops on the market today.