The 14.4 volts is an overcharge on behalf of the charger. This is usually okay for a short time, e.g. at the end of a charge cycle, but if left long term at 14.4 volts trickle the battery will be damaged due to depletion of the electrolytes.
A typical trickle charge would be 13.8 volts would be used as this is the normal 'float' voltage of 12 volt lead acit batteries.
In a 12 volt battery you have 6 lead acid cells rated at a nominal 2.2 volts each, this gives you the 12 volts mentioned.
However in reality this is actually 2.3 volts on a good cell (in the same way as 1.2 volt NiCd's give typically 1.35 volts when fully charged)giving you the 13.8 volts you are seeing. This 13.8 volts indicates the battery will take a good charge.
To determine it's condition you could try 'drop' testing it, this is simply putting a large load on the battery for 15 seconds or so and seeing what voltage drop is measured at the battery terminals, but the value of the load (in some cases 1/2 ohm for large batteries) needed for the drop test will vary for different capacity batteries, and without manufactures datasheets for the performance of the battery under these conditions this could be inconclusive.
You could try ensuring it is fully charged then testing for capacity. e.g. if rated at 8 amp hours, see how it performs giving 1 amp for 7 hours. Beware though that this way you could easilly take the charge too low, this will damage the battery.
Your will also need to know if any conductive sludge has formed in the bottom of the battery. You can best prove this by first fully charging the battery, and then leave it on the shelf for a couple of weeks. When you test the battery after this time it should still have most of its charge. If not, this indicates you battery has been damaged.
I hope this is of some help to you.