Orion Turns over but then dies

Hi people.
Wonder if anyone out there can help me.

My car:
Heap of a 1992K ford orion 1.8 16v Petrol. Manual

My problem:
Sometimes, mostly when car is not used for more than 24 hours, when I try to start it, the starter motor begins to turn, then grinds to a halt.
Brought a new starter motor and replaced battery. I took it to a garage, who said it was not the starter motor and gave it back to me, but said it was a Fuse Box problem. (unusual sounding to me) The garage replaced the fuse box, and the car ran happily-ish for a few weeks.

It has started to turn over slowly again, and did not start at all this morning. I have charged the battery,and it is (for now) turning over quite happily.

In my very limited knowledge and that of my partner, we think it may be a power leakage problem (i.e from the car stereo) that mayb two positive power wires are attached to it. But we are not sure. I have disconnected my stero to see if it makes a difference

If there is anyone out there who may have had a similar prob or who knows about stuff like this, please help.

Thank you in advance to anyone who may be able to share a bit of knowledge.

Thank you

You might be on the right track some stereo systems far outstrip the charging system of the car.
Basically if the stereo is kickass high amperage and the alternator only puts out a wimpy 45 amps or whatever it is. its probably running behind.