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When i turn on my acer 5735z with the power adaptor plugged-in it boots up but cannot continue, it will restart. But when i boot it up without the power adapter or by using only the battery it continues booting up. Where would be the problem? Thanks for the answers.

You could have one of two possibilities. 1. Your power plug/jack in your laptop might be broken. I had a similar situation. The computer would only start with the battery. Switching batteries allowed the computer to work until it drained. I had two identical laptops and I would switch the batteries out to confirm that it wasnt the battery or power cable. After testing the power plug/jack inside the laptop while connected to the power adapter cable, I determined that the power plug/jack was damaged internally and wouldn’t allow the battery to charge properly. 2nd possibility is that the charging/power section in the laptop motherboard might be toast. A motherboard swap would be required. A new/refurb motherboard is the last thing I would change. Just did a quick ebay search and found a few under $30 shipped. Again, last resort would be a motherboard swap.

The problem is your power supply unit, if its a desktop i advice you change your PSU but if its a laptop i advice you change your power cable to the one that can supply more power to the system.

Im getting the same happened to my laptop. At first i thought it was just heating up cuz of the dust inside. then speculated that the windows and drivers might be messing things up so i installed a new windows but the problem still persisted. I read in a forum that i should be able to use the laptop while plugged in if i turn off one of the core of the processor while being in the safe mode. I did that and it works fine. So i thought maybe the processor was the problem, i went ahead and swapped the processor but when i turn on all the cores of the processor; the problem was still there. I even changed the thermal paste on the processor but the problem still remains :/

Can it be a bios problem?

It has to be associated with power. Since you tried another adapter, the issue must be on the MB. Disassemble as much as needed to view the components around the power input connector. Carefully inspect all the electrolytic capacitors looking for any sign of leakage or convex tops. All tops must appear flat or slightly concave. Replace any suspect - which will be easier said than done.