Effects of no ground in wall outlet

You could always just put one grounded outlet where you really need it, and wire it to the incoming cold water supply or to a copper grounding rod. If your audio gear is near an exterior wall, this would be especially easy.

The ground is for safety. Many pieces of audio equipment are operated with their ground connection "lifted" to avoid hum.

Your system will sound great as you electrocute yourself!

Safety AND performance! Most current audio gear rely on a good ground connections to shield the signal from RFI noise, prevent hum, and to drain off digital nasties. Do what Jimmdavis recommends. And analog, OY! Can't do without a good ground for ANALog! ;-)
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If all your equipment is now plugged into one ungrounded outlet and there is not any grounded objects with in arms length of the audio system, imo, it is safer that way than it would be if you installed a dedicated separate ground wire to an isolated outside earth ground rod.

What you should do is hire an electrician to install at least a couple of new dedicated branch circuits.

NEC does allows a 2 wire receptacle to be replaced with a GFI receptacle. A GFI receptacle will still operate as designed if an equipment ground is not present. NEC does require the receptacle cover plate to have a label stating "No Equipment Ground". The cover plate also needs to be plastic or nylon, no metal plate....