A little late to the party but hey...
I have this problem and thought I might put down some thoughts in case anyone else comes across this. I often find forums a good source of info.
I have a Transformer TF300T with the corresponding keypad with internal battery pack. It stopped charging. That is when plugged into the wall outlet it no longer charged. Neither did it charge when the tablet was connected to the keypad and plugged into a USB port of my computer, however, when plugged directly into the tablet from the USB port on my laptop I did get some change into it but with no charge light or on screen indication. Probably a trickle charge. Below is my best guess as to what is happening.
It is important to understand a little about your electrical charging and how batteries charging work. Rechargable batteries have reversable chemical reaction that happens when discharging and recharging. Voltage relates to pressure so that when you use a battery it produces a certain pressure through the electrical circuit to make it work. There is a chemical process that takes place in the battery. To charge the battery you place a pressure in the opposite direction to the discharge which thereby reverses the chemical process so the battery becomes charged. The amount of voltage is important as to little pressure won't work ('wont turn the wheels') and to much will blow it up ('the wheels will blow up')... it will blow up!. Therefore when selecting a charger it is important to match the voltage of the old transformer with the voltage of the new transformer.
The current rating is also important but slightly different. The current relates to the amount of electricity that is going to be available. If your appliance needs 2A to run and your transformer can only supply 1A then you are going to have problems. Your transformer is probably going to stop working, might melt or the like. However if your transformer can supply 3 or 4A to a 2A appliance then you are going to have plenty of current, no problem. So when replacing a transformer or power supply you need to have at least the same of more of the current.
Match the Voltage Rating. Make sure you have at least the same or more of the Current.
The Asus transformer has a rating stamped on it of 5V 2A or 15V 1.2A. Because of the two ratings I am guessing that it has a variable output dependent on the level of the tablets batteries. 15V would charge the device quickly when it is in a low state and this would drop all the way down to 5V to trickle charge it when the device is mostly charged. The device will NOT trickle charge when plugged into the keypad to the tablet. The tablet will trickle charge when plugged into a USB port or in my case I picked up a transformer that is rated 5V 2.1A - an ipad transformer as it may - until I can get a proper replacement. I didn't use the other transformers I have around the house because they were all rate less than the 2A that the original is rated. There is no indication that the tablet is charging as the charging light and internal on screen indication must operate/function only when the normal charger is operating at a higher voltage and I am charging at 5V not 15V but at least I can get a charge into it even if at a slower rate.
I am currently trying to give the keypad a trickle charge but I don't think it will work because as we learnt above to charge a battery you supply a higher voltage - pressure - in the opposite direction to the discharge voltage. Since the keypad when working normally charges the tablet when plugged into it I am guessing that the keypad supplies a higher voltage to the tablet than the tablet itself. This voltage from the keypad will likely be the same as the 5V USB standard which means I am not supplying a voltage to it greater than the discharge so no chemical reaction in the opposite direction and therefore no charging. I will need to get a higher voltage supply transformer.
With regard to the interconnected cable. It is just a cable (guessing) Just a group of copper wires connected to a plug at each end. The number of strands in each cable dictate how flexible it is as more strands means the wires can slide over each other more easily thereby making it more flexible. There may be difference in the quality of the cable and connections and also the rating of the cable to cope with voltage and/or current but it is just a cable. You often only get what you pay for.
Hope this has helped.
P.S. I never turn my tablet off except when there is a problem or an update, so it is always instant on when I press the power button. The one indication I have to know that my tablet is charging (trickle charge) is that when I plug it in, to a USB that will charge or the new ipad transformer I bought, the screen lights up. It doesn't tell me it is charging but it does light the screen up from standby mode or sleep mode or whatever it is called. If it doesn't do this you might have other issues and I have typed all this for nothing.
Have a nice day anyway.