You'll need a hayes manual if your not familiar under the bonnet.
turn key
Q) is there a "click" from the solenoid (might need a head under the bonnet for this)
If yes, cary on, if no, try shorting out the solenoid with a big plasitc handled screwdriver and some rubber gloves. Have someone at the key turn it and short accross the big terminals to see if the starter spins. If this starts it, you need a new solenoid and/or the connectors have corroded/fallen off.
Q) does the starter spin slowly or not at all
if yes – dead battery, earth strap from engine or duff conection somewhere beterrn battery and starter. Or the starter is internally FUBAR.
if no……….
Q) does the starter spin quickly
in this case the ratchet/pin has failed, sometimes this is servicable, sometimes its a new starter required.
MX5's are reliable untill they fail an MOT for rusting through. So a scrapie should have plenty of mechanical spares in good condition as your selling soon lifetime isnt an issue. If you want to keep it plenty of old cars means recon bits should be cheep, if not some places will refurb yours, but this takes time so the cars off the road.