It sounds like there'* about a 99% probability of it being a 1/4 watt resistor. If it'* just a small signal circuit, 1/4 watt will be fine. You can always use a larger wattage resistor in place of a smaller one, unless the smaller one is actually a fusible resistor that is designed to blow past a certain power limit, -like a fuse-. Otherwise, the current intended to go through a 1/4 watt resistor, doesn't care one bit if it goes through a 1/4 watt resistor or a 1,000,000 watt resistor if they have the same resistance and tolerance. It'* like using a 1" garden hose instead of a 1/2" garden hose to water your garden. The water doesn't care.

But larger watt resistors are typically physically larger and in tight circuit boards they might not fit. They also cost more, but since you're just dealing with one, it'* not going to break the bank.

Also, this is just an aside. . .resistors usually don't go open on their own, without something downwind from them going short. Typically a transistor, a diode, or a zener diode. So if you haven't ruled out shorted silicon devices yet, you might look a bit further.