Have a 2012 T100 Bonneville & the starter won't engage. Battery is charged. Recently acquired, I had to jump it to start, so charged battery. Worked fine, sat for couple weeks, now sol

ill answer for NO ELECTRICAL POWER :
sure and is easy with any DMM meter, got one? any $20 DMM.
my guess;1
engine will not crank
dash lamps out.
head lights out. dead.
post systems of electrical system , all parts that work and those that dont work, and problem is easy.
cleaned battery terminals.
tried borrowed battery that reads, 12.6vdc ? (charged is 12.6)
2012 that is in warranty car.... ?
my guess on 2012
jumping a car, that is battery jump starting.
a battery can short, and no jump start on earth will start shorted battery in car. but does lay down some big sparks, or burns up cheap walmart cables.
if the car will not crank, say just that, my starter motor will not crank
jump started from live running other car.
if true then make sure headlights work , if they dont work fix that first.
HL must always work, even keys in pocket.
best is to put a fully charged battery in the car, jump starting can cause
surges that can damage sensitive electronic$$$, do jumps as a desperate measure,
with a charged battery,
1: Head lights work, no fix that , use voltmeter
2: cranks robustly.
no , wiggle shifter lever, (on A/T cars the park switch blocks cranking) On M/T the clutch blocks cranking.
with any dMM
measure battery voltage before crank and during.
12.6v good. reseted.
cranking.
0 to 10v bad (weak battery or shorted starter motor)
11 and above good. and must crank, if not , starter is bad.
to prove starter is bad, check voltage at starter solenoid coil wire lug.
it must be at 11v cranking , below 8v it chatters, and fails.
if at 0v cranking this lug that means the Key start line is failing.
A/T switch not closes, or bad ignition switch.

Alternator doesn't have anything to do with starting the car, it supplies power to the system once the engine runs. Does your starter crank the engine? Do you get spark? Is fuel pressure correct?

You need to charge your battery up more. Either get a battery charger or leave the jumper cables hooked up for a longer period of time.
Your battery was probably completely dead. You might even need a new battery...they really don't like to be completely drained.

damaged starter switch

It is probably your cellinoid try jumping your starter

Could be a failing starter or problems with the cables.
A dead cell in the battery will do it too.

Hi Vernon, There could be a number of different reasons why your vehicle is failing to start. The battery voltage could be dropping during start and become unable to engage the starter motor to turn the engine. You can check this by trying the key with the head lights switched on. If the lights become very dim, you'll need to check the battery, meaning clean the terminals and then try to start with a jump from another battery. If you achieve start up and it fails again the following morning, you will probably need to replace the battery. There could be a problem with the starter relay or a loose contact for the starter motor, most lik3ely the one connecting to the soliniod. It would be good to know some additional information, such as does a clicking sound come from the starter when engaged? Is there a perceptible drop in voltage output when the starter is engaged? does the enine turn at all? Try what I've suggested and if that does not solve the problem answer the questions and let me know anything else which you may think is relevant. Regards John

Those are the typical symptoms of a weak battery. Try either to charge the battery, try a jump start or replace the battery. Lights or horn working do not give an indication of the battery charge status.

This could be several things....how old is your battery? if it isn't holding a full charge it sometimes won't have the cranking amps to fully engage the starter. It could be the solenoid or the starter itself but I would start with the battery.