Play buttons are usually arranged to stay in the down position until the tape reaches the end or you press them - the locking mechanism is released. Your locking mechanism is probably clogged up with the dust of ages.
Either take the case apart and attempt to clean it up or give it a SMALL squirt of WD40 oil and be patient for a day or two - do not be tempted to keep squirting oil into the box else you'll cause bigger problems.
Peccavi
February 2013
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