1998galaxy2.3i

98000 miles, well maintained. Today after hot 200 mile journey failed to engage reverse in drive at home although reverse had been employed during the journey. Inspection of zone under the fabric boot (encircling the gearlever) shows that there is no problem with the visible lifting "gate". The gate is lifting successfully but the gearlever cannot even be forced into the "reverse" position. Any suggestions very welcome. I fear that this is an expensive gearbox task (several hours' labour) on an otherwise very reliable car.