If it will run with the power cord plugged in but the battery won't charge your battery has probably gone bad. They will only take so many charges and they should never be run down all the way - that causes them to take even fewer charges. You may just need a new battery. It's always best to use the battery only when you have to and keep it charged as well as possible.
If the machine won't run when the power cord is plugged in you can try this: remove the battery and power cord and press and hold the power button for a couple of minutes. Then reinstall the battery and the power cord and try again.
If neither of those work you need to take it to a shop or send it to ASUS for repair.
Since I don't have a budget yet and needed a laptop asap, I chose to buy Asus x453m while I accumulate enough money to buy a powerful one. Did my research about it and on entry-level (processor, sound quality, USB 3.0, smart touch pad, etc.) , it is one of the best.
However, I was disappointed when I've discovered that its battery is built-in not to mention (found after newer reviews were released) a meager 2-cell lithium battery to which when run at power saver-battery mode, only lasts 3 freaking hours! And since its built-in, if a problem occurs regarding the battery, you have no choice but to bring it to ASUS or your local repair store or buy a replacement batt which is challenging btw. Going mobile -road warrior style is also out of the question.
Tip: Do not fully charge and consequently discharge the battery as it is lithium-based. Li-ion batteries hates that. Maintain a discharge threshold of 20% and a maximum charging threshold of 80-90%. That's how you prolong a battery's life especially on built-in ones like your laptop.
I basically write which means I rarely stress out my laptop's quad-core processors. Sadly, even under really light tasks (browsing, word processing, and playing music/video simultaneously), core temps averages at Idle-50*C levels, light load 60*C levels, and when pressured a bit, quickly escalates at 70*C levels. This is really annoying for me.
Anyway, in general it performs well and I can't whine because this is what should be expected on an entry-level laptop.