Hi! I'm Dan, I'm from Wales.
Back in the day, the European grid was at 220V and the UK grid was at 240V. This was changed in the 90s to harmonise the grids so they could be interconnected, with both now being 230V. This change is less than 5% in each direction, which should well be in the tolerance of all the components in your computer. The EU regulations have actually always allowed for fluctuations larger than this, too. I highly doubt that the small increase in voltage is what's to blame.
The power switch is integrated into the PSU unit on the XT - I imagine there's a fault in your PSU somewhere such as a failed capacitor, blown fuse, or something like that. The switch itself is probably just fine, it's just some of the components it's connected to! It happens - Capacitors fail as they get old, power surges blow fuses, it's all just a part of owning a vintage computer.
If you're not confident with your own diagnosing and soldering, it's probably best get your PSU sent to a specialist for repair, or buying a replacement power supply. No need to modify for 230V at all. 🙂