This is likely to be a recurring problem, so I think it is a good idea to keep this thread alive. I came across this thread because I have also just had, and solved this problem, however, my solution was a little bit different so I'll make my contribution as well.
The short version:
Try another PSU.
The long version:
When this started to happen with my 10V, I noticed that while it was happening, the 10v thought it was running on battery power (which it was not). When I unplugged the power lead, the screen backlight went a little bit dimmer. When I plugged it back in, it got a bit brighter again. So DC power of some sort was definitely reaching the 10V.
My Dad also has a 10V which he has hardly ever used, which is a shame, but it meant that I could borrow his PSU for a test. Using his PSU totally fixed the problem. If you aren't technically interested, you can stop reading now and go and borrow or buy another PSU to try. But if you want to know what was wrong with the original PSU, read on.
I'm an electronics technician by trade, so I decided to dig a little deeper. First of all, I checked the output voltages from both PSU units when they were unloaded, that is, with nothing running on them. Both were producing a nearly perfect 19V output.
I then took them to work with me and ran each one in turn into a high-power 12 ohm resistor, that being just about the right value to force the units to supply their maximum output current of 1.58 Amps.
My Dad's PSU: The output fell from 19V unloaded to about 18.7V fully loaded. That's normal.
My original PSU: The output fell from 19V unloaded by a full 5 volts to 14 volts, MUCH too low. Clearly something wrong there.
Loss of performance in switched-mode power supplies like these is nearly always caused by the failure of one or more electrolytic capacitors, so I split the original PSU open expecting to find it full of sick capacitors. To my surprise there were only three in the entire unit and all were in perfect health.
I then wired the high-power 12 ohm load directly to the DC output of the PSU PCB, via short, thick leads, bypassing the long DC power lead. I found that the PSU was then able to maintain 18.8V across the load. Moving the load back to the other end of the DC power lead, I found that I had 18.8V on the DC output of the PSU PCB, but only 14V across the load at the other end of the DC power lead. If I wiggled the lead around while monitoring the voltage across the load, the voltage reading went wildly unstable, shooting up and down, but always returned to a low value once I let go of the lead.
Verdict: PSU electronics / PCB OK, but DC power lead faulty (high resistance).
I have always been careful not to wrap the cable tightly around the PSU when it is not in use because that tends to make cables snap at the places where they are always bent around the sharp corners of the enclosure. But, I do keep the PSU in a pocket in the sleeve that I keep the 10V in, and to get it in there I have to coil the DC cable up into a four inch diameter coil. With hindsight, I believe that the constant coiling and uncoiling of the cable has damaged the cable conductors, raising their resistance to such an extent that the voltage drop across them is now too great during times of high current demand, such as when the unit is both running and trying to charge the battery at the same time.
I could have fixed the original supply by finding a new thick DC power cable for it and putting the PCB safely inside a new enclosure, but third-party 'Genuine' replacement power supplies are widely available at reasonable prices. I ordered one and it works Ok - the main difference between it and the real thing is that the replacement does not have the white power on indicator LED built into the plug the way the original PSU did.
Nor does it actually have to look anything like the original, as long as it meets these specifications:
-Exactly the same size / shape DC power plug on the end of the DC lead
-Positive on the inner/centre contact of the plug, negative on the outer contact of the plug.
-19V DC regulated output, capable of 1.58 Amps or higher.