Bike is completely dead

The fact that the neutral light does not show up on the dash may indicate that the gear position indicator is not calibrated correctly. Does the bike start with the clutch pulled in?

Check the brake light switches, especially the rear,
and basically the whole wiring harness, including any accessories.
Those problems can be tough to solve.

I had the same problem on an XS 650 Yam. (at 70 mph) .All that was wanted was a pair of new bushes.As these were worn there was no charge going into the battery. Hope yours is the same. Baz

ORDER A CLYMER MANUAL FOR YOUR BIKE!!! Everything is easier to inspect with the fairings and accessory covers removed. While you are waiting for the manual, trickle charge your battery. Make sure your charger is a maintainer as well. It charges your battery and keeps it conditioned. Keep in mind, even if it's a new battery, they are not impervious to fault. When you get your manual, two or three days later, the battery should have a full charge as indicated by a green light(normally) on the trickle charger. Now, key your ignition on and get your multimeter. Read for battery voltage on the down side of your ignition switch.Then measure and note the draw from your battery as you hit the start switch. Open your manual and start reading through components like your rectifier, coils, main power fuse (probably a 30A)on your fuse box. Remember, a bad ground within your electrical system will report a failure to allow passable current to the components that need the juice. Look for corrosion or gunk on the contacts of your electrical components. Good luck, let me know how it works out.

A bike of that vintage should have 10W40 in the summer, and 10W30 in the winter.
Check your fuses for the starter issue, and also check the neutral and clutch safety interlocks.
Most bikes won't start is they think they are not in neutral or the clutch isn't pulled in.

Actually when the key is turned on all the "dash" lights come on neutral, oil, temp and what ever else as soon as the bike starts the lights will go out. If the lights come on while the engine is running then you have a problem or it's in neutral "green".

For the bike not starting a few things, first off the battery even though you say it's new may have been sitting on the shelf for a while and they do loose power so it may need charging. The newer bikes the headlight light comes on when the key is turned on which robs the starting system of power to turn the starter, the batteries need to be good on these bikes or it's just not going to work. If the headlight comes on and looks yellow or amber then there isn't enough power in the battery. If it's a nice bright white light then there is power and the starter may need to be serviced.

If the bike has been sitting over the winter I'd guess the battery has just lost power and requires charging.

Cheers be safe and have fun with your motorcycle

MAKE SURE THE BATTERY IS IN A GOOD STATE OF CHARGE, ON THE OLDER BIKES WITH AC LIGHTING THE BATTERY ACTS AS A RESISTOR, HENCE IF THE BATTERY ISOLD AND NO LONGER WORKING, WHEN YOU RUN THE MACHINE ALL THE BULBS WILL BLOW, STARTING WITH THE NEUTRAL LIGHT, AND SO ON, AS THE BRAKE LIGHT , HORN , AND INDICATORS ALL WORK ON THE DC ELECTRIC SIDE IT WOULD PROBABLY BE A GOOD IDEA TO CHECK YOU ARE GETTING 6VOLTS FROM THE BATTERY TO THE IGNITION SWITCH, YOU COULD LOOK FOR BROKEN WIRES AROUND THE HEADSSTOCK AREA, OR CORRODED BLOCK, AND OR BULLET CONECTORS ALSO IN THE COMPLETE HARNES.

Make sure the battery is fully charged and the battery connections are free of corrosion and tight. A fully charged 12 volt battery should read at least 13.25 volts. Also check the fuses, making sure each one is not 'blown' and is making proper electrical contact in the fuse box.
If the above items are correct but it still won't crank over with the electric starter, locate the starter solenoid and - using a large screwdriver - carefully touch it across the two large cable connections on the top. If the starter spins over, then you've got a bad starter solenoid. If you've got voltage to the top of the solenoid and the starter still doesn't spin, then you've got either a bad starter motor or a bad electrical connection going to it.

take your battery and have it tested. just because you have voltage dosnt mean its there under a load