Is what the questioner did—limiting himself to dry ablution (istijmar) with tissues, then wiping the area with tissues moistened with a small amount of water, then drying it, and then praying—valid, knowing that the water supply was cut off for seven hours?

If you have used tissues to remove impurity three times or more, and you predominantly believe the impurity has been removed, then you have fulfilled your obligation, and you are not required to use a wet tissue afterwards. If you are unsure about the discharges, consider them to be from the natural moisture of the vagina. However, if the dry purification (istijmar) was not permissible (fewer than three wipes), then the area has not been purified, and your use of a wet tissue necessitated the use of water. Your prayers are valid in all cases as long as you were unaware of the ruling, given that avoiding impurity is a condition only with knowledge and ability.