With electrical issues always helps to start with easy bits first, then move on to complex.
1. Battery. Sounds like it's holding up OK charge and power wise... as it managed to turn the motor over numerous times. Still after having done all that hard work a good proper charge on a trickle charger will surely do it some good. You should hook the battery up to a trickle charger whenever your not using the bike for more than 5-7 days at a time.
Nonetheless, first check to see if the leads are loose on the battery terminals, they need to be nice and tight. Don't use a screwdriver to tighten them, even though the bolts have Philip's grooves, use a proper wrench as they also have a hex head... 10 mm I believe.
2. MFI. This is the flashing code your FI light conveniently threw up for you but whose usefulness you were unfortunately unaware of. It provides info on parts of the fuel injection system that may have suffered from some failure, either permanent or intermittent.
The code consists of a series of long and/or short flashes, then a pause and if there's more then one error/failure another series of long and/or short flashes, a pause and so on. When there are no more errors it will repeat the same ones over again "ad libitum".
One long flash (1 second) = 10 points.
One short flash (<0.5 seconds) = 1 point.
Add them up (up to the pause) and then check the number on the chart in the Workshop Manual, you can download it on this forum in the download section. There's also a tutorial on here in the how-to or maintenance section which explains how you can bring those codes up at will. This way you may be able to go straight to the needle in the haystack.
3. Known weak points in the wiring harness. There was a Honda recall on all 6th gens to have the front subharness replaced and any other parts of the harness and recharging system that may have suffered as a consequence. Check w dealer whether yours has had that done.
4. Check the usual suspects of the wiring harness. These are a few connectors known to fail and burn out. I believe there's a thread detailing all of these somewhere in the forum:
- Check out the engine kill switch, big red switch on RHS handlebar. It often fails due to grime and/or corrosion. Open it up a and give it a good blast of contact cleaner or WD40.
- Check all wires and connectors and fuse holders and relays in the battery bay under the seat. Remove rubber coverings and inspect for burnt components and signs of overheating. Replace whatever is untoward looking. There is a tutorial on here somewhere explaining improvements that can be made.
- Big blue connector on LHS, just forwards of the LHS radiator. Check where the green ground wire goes through this connector first, but check them all anyway. If it's burnt out and you can't get Honda to fix it under the recall, just solder-splice a 12 gauge wire to bypass the connector while also running the wire w a ring terminal to the closest spot on the chassis.
While your there check the big grey connector next to the blue one just in case.
- The famous "Eurethra" yellow or orange ground wire bus connector on the front harness. It will be yellow for 02-05 and in the front harness proper, wrapped in black electrical tape in the left hand grouping which runs along the LHS arm of the metal bracket which supports all the fairing and optics. It has approx 10 or 12 thin-gauge green ground wires running through it but fails tremendously in providing continuity.
On 06-10 models this connector is orange and located in a more convenient spot inside the rubber protector together with the blue and grey connectors mentioned earlier. I think Honda relocated it to improve access but continue using the same crappy connector as this generates work for dealers.
You will have to remove the LHS fairing for the blue, grey and orange connectors and if it's an 02-05, the front nose fairing as well for the yellow one.
Common practice is to cut this fecker out and solder the lot with a soldering blowtorch... A regular soldering iron won't do it as it's a large mass of wires. You could come up w other valid solutions so long as all wires lead to Rome (which happen to be the green wires that run through the big blue and grey connectors mentioned earlier).
- Big white connector on RHS on top ridge of the RHS radiator. This has three yellow wires running through it from the alternator to the regulator/rectifier. Often burns out due to corrosion or bad fit. Cut it out and use a good quality ceramic screw-down type connector rated for high current and voltage, or hard-wire it (solder the wires directly).
It would be useful if you had a multimeter and checked continuity of wires running through these connectors and switches.
If all the above checks out good, check out the wiring leaving the ignition at the top triple/yoke, where the key goes... seen more than one case of broken wiring leaving circuit open when turning the handlebars.
If your bike has HISS (doubt it), check the wiring.
Otherwise at the worse it could be stator starting to fry. Check the tutorials out on here. Rarely does the R/R fail on 6th gens but... Suspect stator first, then R/R