As you have mentioned in your very first line, the battery has been sitting in storage for a period of 10 years. I’m quite sure there has been a lot of sulfation of the plates going on during this period. This damages the plates of the battery quite significantly. Is your battery a Sealed Lead Acid battery or is it one of those flooded 6V motorcycle batteries?
I have tried restoring some fully dead more than 10-year-old lead-acid cells by topping it distilled water and adding three drops of battery acid to increase the conductivity (since your battery is charging you don’t need to add any acid). This helped to increase the charge holding capacity to a good extend. One thing to check is to shake mildly your battery if its VRLA and hear for something moving at the base of the battery when shaken. If you can hear something moving then the lead particles from the plates have disintegrated and are settling at the bottom of the cell and this causes shorts on some cell chambers. Now if your battery is like one of these conventional distilled water topped old automotive batteries then you can see it through the case. I think this might be the reason why you are getting only 4.5Volts.
A single lead-acid cell can output around 2.1-2.25V. A 6V battery is made of three 2.2V cells in series. So, one of your cells is likely shorted out or the battery acid in that cell had dried out. Try adding water to all the cells and then charging up. If you feel the heat building up in any of the three cell chambers (can be felt on the battery surface) then the battery is ready to go to recycling center. If you turn lucky and the battery manages to charge up finally to get fully charged to 6.45V. Then you may need to cycle the charge-discharge cycle a few times to build some capacity. But even then a significant part of the capacity will be lost. You may need to load test it to see the exact figure. Hope this helps.
As for your charger that you have stated above giving only 0.15V. Is it a smart charger? What brand and model is it? Try using a traditional charger that can give output no matter the voltage of the battery. Like a car/ bike charger with 6V setting. Once it’s above 5.98 to 6.12V then you can continue charging the battery with your present charger and keep checking the voltage to see if it has increased.