As a possible alternative to coachgeo's post, if it doesn't suit you to go to the store to have your battery tested, you may be able to do some extra testing to get by. If you have another charged battery to jump from, remove the ground connection from your battery in the tractor and connect the negative jumper cable to this ground cable, doesn't matter if it hangs or sits on the tractor as it is ground, as long as it doesn't connect or touch the ground terminal on the tractor battery. Then place positive jumper between both batteries, then hook up the negative to the jumper battery. Now you have your tractor connected to the "known good" battery.
Check battery voltage with multimeter, then start and run tractor and check battery voltage again. Hopefully your battery voltage will see an increase. If it doesn't, then you still have a problem. If it does increase and start charging, it shows your tractor battery is in poor condition and your charging system cannot cope with it.
Most "alternators" use the charge lamp to self excite the alternator and if it is blown, the alternator does not charge.
However your "dynamo" is outputting 35 volts so is OK, (as previously mentioned by 85Hokie) and it's possible that your regulator needs either a B+ signal to work, either through a lamp/bulb circuit or direct from the start switch. So test to make sure you have 12V+ at the regulator when the key is on, engine not running, also that your regulator has a decent ground, not through paint etc. I would also expect to see 12V on the lamp circuit.
Remove the charge lamp and test across 12V to ensure it is good.
Also have a look for an inline fuse under the dash that feeds the charge lamp circuit, as IIRC, Kubota did that with a few of it's tractors.
How many terminals does the new regulator have, and what color wires go to each terminal. They should be numbered in the plug.
