Morris Minor Owners Club

When you tried starting you could have stressed out the starter motor, but i've done what you have done once or twice and its been fine - the lights i don't know about! Talk to an expert (someone like Cam/Ray/Gareth or the other knowledgeable people!!!!!)

Chris,
It sounds more than likely that the starter motor pinion is jammed in mesh with the flywheel ring gear. At the rear of the starter motor (towards the front of the car) you will see a square shaped piece in the centre (it might have a cover fixed over the top, but it shouldn't have on a Minor). This is the end of the starter pinion shaft. Turn this using a spanner & the pinion gear should release.
This is the most likely explanation, although it doesn't explain the ignition/oil lights not coming back on.

Do the rest of the car lights go out (eg, the side lights)?. If it is just the dash lights that go out, then that's odd and not something I've come across.

There's 2 things I can think of that may be worth checking:
1) Bad connection at the battery / or on the battery leads at either end. Trying to crank the engine over will draw high current which itself can make a poor connection go very high resistance.
Maybe when you disconnected / reconnected the battery you disturbed the faulty connection enough to make it work a little.

2) stuck starter as Scot described above. He's right to say that it shouldn't cause the lights to stay off (unless you also have a sticky relay - but if yours is a pull start then there's no relay).
If you want to check this without tools, then put the car in 4th gear and try to move the car. Normally it is easy to move the car and turn the engine over in 4th - if you can't turn the engine over then 99.99% sure that the starter is jammed. Use a spanner on the end or just jog it backwards and forwards in 4th gear until it comes loose.

Check the big earht strap under the car, too... that could have come adrift, but that's about the only thing I can think of.

Check the big earth strap under the car, too...

Ah yes - that one's always the last to be checked, and therefore the most likely..
If in doubt, connect a jump lead from the negative battery terminal to a good earth point on the block. That's a useful tip on Euroboxes too, as the earth strap isn't always easy to get to.
[If you are positive earth - use the other battery terminal]