The stuck CAPS LOCK LED suggests the keyboard scanning is FUBAR, or the keyboard itself is in need of some TLC. The white noise is normal if the volume pot has been turned up to eleven, unless there's something wrong with the SN76489 sound generator chip...
As I recall, keyboard scanning is done with one of the 6522 VIAs (probably the System VIA). I'd start by swapping the User and System VIAs. That'll prove if you have a dead VIA (or not).
Next -- check for stuck or dirty switches on the keyboard (BBC series machines are real swines for this). Also check the motherboard links (jumpers) are set correctly.
If your machine was from the BBC Master series (e.g. Master 128, 512, ...) I'd suggest replacing the CMOS battery, resetting the config (DEL-power-on or R-power-on -- one is for RISC OS, the other is for BBC MOS, I can't remember which is which) then configure it using the settings from the Welcome Guide.
Also, I think R J Sprowson (Sprow) has some troubleshooting hints on his website. I'm not 100% sure if they're Master-specific or cover the B as well...
