Wow! That takes me back a few years (and more)!
Are you talking cassette type or reel-to-reel here? The following answer applies to reel-to-reel.
If I remember rightly, there is a spring-loaded capstan that the tape passes round and if there is any drag on the feeding spool, the capstan is pulled across and activates the stop mechanism.
If your machine is cutting off after a few seconds, then there must be an excess load/drag caused by the feed spool. Check that it is turning freely and lubricate if necessary.
If you are able to feed the tape through by-passing the tensioned capstan, then the tape will play, but the extra drag may cause it to be slowed and consequently lower the tone of what is being played. The other danger is when the tape reaches the end - it won't cut out so will excert undue tension on the tape that may stretch it or snap it (apart from possible damage to the machine).
If you are using a cassette type machine, then the excess drag is likely to be caused by uneven laying of the tape around the spindle within the cassette. I suggest fast winding right to the end and then fast rewinding back to the start before trying again. That should lay the tape more evenly.