Welcome to Android Central! The battery might have completely discharged, which is death for a lithium battery. Since it's so old, that might have made it that much more likely to happen.
Leave it plugged into a wall outlet undisturbed for at least 6 hours. Then press and hold Power for about 30 seconds, and see if it boots up correctly. If it doesn't, then you'd probably have to get the battery replaced (although I wouldn't bother with such an obsolete phone).
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