If computer equipment has an NBV of zero but is still in service, does property tax still need to be paid? Also, how do a calculate the gain/loss at disposition?

The property tax on computers is usually assessed on a declining basis and continues to be assessed even when the asset has Zero Value. For example in state of Virginia, the following represents property tax assessment computers.

"The City assesses computers at 65% of the property purchase cost in the first year of service, 45% the second year. 30% the third year, 20% the fourth year and 5% the remaining years"

Source:Business Personal Property Tax

Regarding your second question, the calculation of gain/loss at disposition of the asset is based on the following factors,

1) How much you sell the depreciable asset.

2) How much was the original cost and how much depreciation has been taken on that asset. Clearly, if the asset has been fully depreciated. the asset has a Zero Basis. A partial depreciation means that the basis of the asset would be the original cost less the depreciation taken on the asset.

The gain/loss is then calculated as the difference between the Selling price of the disposed asset less the basis of the asset. If the asset is disposed for a Zero value then the loss would be the difference between the original selling price less the basis in the asset.

If the asset has been partially depreciated then there would be ordinary loss on the dispostion. Whereas, gains on the dispositon of business assets would be treated as a capital gain!

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