If the problem went away by re-installing the ROM there is a pretty good chance it will return. Pressing on the board to plug in the chip flexes it temporarily fixing cold solder joints. The good news is that the problem might not be a bad part which could be hard or impossible to find and replace. A lot of times bad solder can be fixed by just reflowing it; touching it with a soldering iron and adding new solder. The bad news is that it can be tricky figuring out which connection is bad and many of them on the G2 are extremely small so you need a good soldering iron to handle it. Since the device still passes audio but has an unresponsive UI the problem is probably related to the z80 processor. There are address and data lines that run between the z80, the ROM and SRAM which would cause this kind of problem if broken. The z80 also connects to the Lexichip and 2186 but I don't think that problems there would affect the user interface. The z80 also handles midi so lack of midi control is another indicator that the z80 crashed. Sometimes the solder connections get tiny, almost invisible, cracks but I've also seen chemical reactions from flux and other substances on the board to cause weird growths to appear and interfere with the connections. They are rare but I've personally observed a case where the chemical reaction caused a low resistance path to be created between adjacent etches. The board literally grew new etches. Weird stuff.
If you know how to use a soldering iron, it's worth doing a close inspection of the motherboard under a bright light and reflowing any questionable connections but it's easy to mess things up so care must be taken.
One thing I was going to ask was if you'd had the problem show up when you were using the G2 in more than one venue. The power supplies on the G2 are pretty good but brown-outs (brief interruptions in AC power) could cause unexpected behavior like this. This can happen if you have an electric heater or some other big appliance on the same power line as the G2.