Battery won't charge

it sounds like one of three things:

1. Battery itself no longer functions
2. Laptop Charger has inadequate amperage
3. The motherboard is defective (most likely).

If you have another battery, or a friend with the same battery, you can try that first (and someone else's laptop charger).

If the problem is the motherboard, you can try to have it repaired but I don't trust many companies to do this kind of work. I outsource my motherboard jobs to a company called Laptop Rescue (http://www.laptoprescue.com/laptop-repair-2/). Coincidentally, they also sell laptop chargers in case that's the problem. Hopefully it's just a charger or battery issue and not a motherboard.

http://www.aurabuy.com/cheap-4400mah-battery-for-acer-travelmate-4740-4740g-4740z-4750-5335g-5335z-5340g-5542g-6495tg-8473g-8472t-tm5740-paypal.html

Not really following your story.
When you say it will not start, the starter would only affect things if the engine will not crank.
If the engine will not crank, you would need to know if the battery is fully charged and if the starter has power and ground.
If the battery is low, something may be draining it overnight. If the battery is charged, the starter should have power.
The neutral safety switch or key switch could be the problem if the small wire on the starter has no power when the key switch is in the start position.

I had a similar problem with a laptop years ago...Where the battery terminals connect to the motherboard, and Im not sure about yours because the models are obviously way different, but in some, they use "battery boards" that connect to the motherboard and are seperate from the system. Those "battery boards" have lots of micro capacitors and resistors on them and are responsible for charging the battery and completing the power circuit to "start" the computer. If I took the battery board out of the laptop I had, the whole thing wouldn't work. Since your laptop is starting while plugged in, but the battery is not charging...I would look into this area first. I am going to rummage around to see if I can find a schematic of your laptop and maybe some parts info.

No danger involved, just useless. If ONE vehicle won't jump it, there's something drastically wrong with the engine. A charging system will only charge a max of 14 volts when charging a low or dead battery. Over that will hurt something. If you have two vehicles connected to your low battery, there's still only 14 volts going out from them and into yours. There is no reason why one jump vehicle won't charge and start your vehicle. Unless of course the jumped battery is really bad or has a bad/dirty connection. So clean your terminals before a jump. You may not need a jump.

Now you have a good battery & a starter that turns over the motor

Have you cycled the key on & off with a fuel pressure gauge on the
fuel rail?

Do you have a fuel filter that isn't over 3 or 4 years old?

Have you checked for spark while cranking ? Use an old plug on the wires,
if you have ignition wires,don't ground the wire without resistance

If you removed the ducting & MAF Sensor it won't start

Tell us what you checked & exactly how that was done.

need more information, does it crank, and not start? Or no crank? If it cranks and does not start, the first suspect would be a crank sensor, they do that...if it does not crank, the battery has to be charged first to get it to crank-we can go on from there...

sounds like a problem with the ignition barrel.the wiring is loose or the connectors are loose or the barrel is faulty,unless thse are all run from the onboard computer.

Testing the electrical circuits an componets is the way to find the problem , not guessing . Testing power an grounds . Voltage Drop Testing the Charging System Plus this charging system is computer controlled .Free wiring diagrams here http://www.bbbind.com/free_tsb.html Enter vehicle info. year , make , model , engine size . Under system click on engine , subsystem click charging system .

bad ground wire on battery.

though if it was a problem it would have blown the 10amp fuse????Don't rely on on whether the bike will start at a gas station to determine if the charging system is working. Get the multimeter out and do a proper test. Should be getting about 14.5 volts @ around 3K RPM. It's too easy of a test to to just skip. If it is charging then start looking for something else. Was the new battery properly charged to begin with? Loose battery connection? I suppose the GPS could be too much but you said that it was dying last november so I would suspect something else. P.S. you need a properly charged battery to get an accurate reading for the charging test. ,,,