Laptop Toshiba A60 - Heats Up, goes off after running 20 minute

If the laptop battery is more than 3 - 4 years old then the battery could be worn out. Rechargeable batteries have a finite number of charge and discharge cycles and will lose their charge capacity over time, i.e. won't charge to 100% and gradually the charge reduces until the battery won't charge up at all. OR The battery shows a 100% charge but when the adapter is disconnected the battery drops off to zero capacity in a very short time. If the battery drops to an unacceptable charge level then the battery needs to be replaced. Rechargeable batteries will fail if stored in a discharged state for long periods.

Try to change the cmos battery?

From what you describe and assuming the new battery was "new", I'd say you have an internal short which is draining the battery over a short period of time. I'd also investigate the accuracy of the battery charge indicator. Download this free utility which will give you a more accurate picture of your battery:
http://www.mioplanet.com/products/batterymeter/

I'm assuming you gave the battery a "commissioning charge" when you bought and used it?
If not, this is something you should do with all new LI batteries. This bit is reproduced from a website that sells batteries for the Toshiba satellite series:

"2. The new Toshiba Satellite a205-s4777 battery pack needs to be circled (fully discharged and recharged) three to five times to reach its optimum performance.
3. Toshiba Satellite a205-s4777 battery will undergo self-discharging when left unused for a long period of time. Thus, it should always be stored in a fully charged state and kept in a cool, dry and clean place.
4. It is normal if the new Toshiba Satellite a205-s4777 battery gets warm when being charged or used. However, please pay special attention if the battery pack becomes excessively hot. This may indicate there is a problem with the charging circuit of the electronic device. Please consult a qualified technician if necessary.
5. To maintain the optimum performance of Toshiba Satellite a205-s4777 battery pack, it is highly recommended to circle (fully discharging and recharging) it at least once a month.
6. New batteries are hard to be charged. Sometimes, your electronic device may indicate a fully charged condition about 10 to 15 minutes when Toshiba Satellite a205-s4777 battery pack is being charged for the first time. When this happens, remove the battery pack and let it cool down for about 10 to 15 minutes then repeat the charging procedure. Sometimes, the new Satellite a205-s4777 battery will suddenly refuse to be charged. If this happens, a suggested solution is trying to remove the battery from the device and insert it again. "

You may have a bad DC connection:

Symptoms of a broken power jack
1. If you wiggle the power cord or the AC Adapter connector on the back of the laptop, the power LED and battery charge LED start to flicker.
2. Battery will not charge in the laptop.
3. Laptop runs fine off a charged battery.
4. With the AC Adapter connected the laptop appears to be dead.
No power LED or battery charge LED activity.
5. Laptop randomly powers off without any warning

If your laptop is out of warranty, then you can fix the problem by resoldering DC-IN jack on the system board. If it

I’m happy to assist further over the phone at https://www.6ya.com/expert/joe_8b8c2cd6ce148309

The very first time you charge your battery YOU MUST CHARGE IT FULLY!!! If you didn't, that is probably the problem.

Also, even if you charge the player for just a couple of minutes it will APPEAR to have a fully charged battery when it actually doesn't.

Most portable media devices require at least 20 minutes to an hour to fully charge whether the screen shows that it is fully charged or not.

You've got a faulty battery. Try another replacement battery immediately, or you might damage your laptop unit.

Obviously, your battery has degraded. You will have to purchase a new battery. And you can remove old programs that you dont use any more to free up space. Defragment the Hard disk to improve performance. Remove unwanted programs from startup. This will improve the speed of your PC

It looks like some divece in your laptop dont pass POST test. Tech support from Toshiba required

Is it turning off by itself after being on for 20min... each time? I.e. is it consistently turning itself off after the same amount of run time? Check the bottom of the laptop... how hot is it? Might be an over-heating problem. Some freeware (MobileMeter) might help you monitor temperatures and see if it is a problem

MobileMeter
http://www.softpedia.com/get/System/System-Info/MobileMeter.shtml

Some excellent heat management information here:
http://www.technowledgebase.com/2007/07/03/monitoring-your-laptops-temperature/

We can only assume that because the cd drive operates then the motherboard is operating in part, although, the southbridge chip may be damaged, as the northbridge works memory etc. Maybe it is that the processor is fried as there is no fan and the system then shuts down. Toshiba are probably half way there with the answer, unless; they investigated further and decided it was not the processor but the motherboard.