AC adapter issues

i have a fujitsu lifebook T4220 and i have been experiencing problems with the power cord. theres an indicator to show when the computer is getting power from the wall, and randomly this started going off even when the computer was hooked up to a working outlet. basically this means that at random the laptop will just stop getting power from the outlet.

so i ordered a new a/c adapter after the other one stopped working at all, and it worked fine for a few hours until it did the same thing. i plugged it back in and its working as i type this now, but obviously it cant be an a/c adapter issue if the new one is starting to have the same problems.

i must note that the battery on my laptop only holds juice for about 60 second so i always have the laptop hooked up with a power cord. hence when the laptop decides to stop picking up power from the wall it immediately shuts down into hibernate.

any help would be greatly appreciated, i have no idea what to do and i can't afford to lose whats on my hard drive.

CPU Fan filled with dirt, dust, or lint. Too much heat. Loose connector, a memory module that is not quite up to par... mismatched memory modules... Corrupted Windows or other files... the list can be a long one, and there is no one cause...
But running it withour a normally working full capacity battery isn't helping anything.
Might be time for a new clean install... then keep good WRITTEN notes as to what is going on when it happens.

Battery Tips to Prolong Your Fujitsu Lifebook T4220 Battery Life

* A new lifebook t4220 comes in a discharged condition and must be charged before use . Upon initial use (or after a prolonged storage period) the lifebook t4220 battery may require three to four full charge/discharge cycles before achieving maximum capacity.

* New fujitsu lifebook t4220 batteries are hard for the device to charge; they have never been fully charged and are therefore "unformed". Sometimes the device's charger will stop charging a new battery before it is fully charged. If this happens, remove the battery from the device and then reinsert it. The charge cycle should begin again. This may happen several times during the first battery charge. Don't worry; it's perfectly normal for the lifebook t4220 battery.

* Do not leave the lifebook t4220 battery dormant for long periods of time. We recommend using the battery at least once every two to three weeks. If the lifebook t4220 battery has not been used for a long period of time, perform the new battery break in procedure described above.

* The replacement lifebook t4220 fujitsu battery will often be higher than the original lifebook t4220 battery. A higher mAH rating is indicative of a longer lasting (higher capacity) battery and will not cause any incompatibilities. A Hi-Capacity battery will, in most cases, outperform the original by 30% to 50%.

see details here