I had a similar problem recently,lots of noise with a popping sound that grew louder then faded,on my export radio.
i turned off every device in the house,the noise gradually went down bit by bit,especially after the pc,monitor,keyboard and the switch mode psu it uses were turned off one by one.
but still had plenty of noise there with this popping signal every so many channels that rose from the noise at about s3 to s9 then gradually faded back to s3 every 30 seconds or so.
i even changed the psu for a linear type i had just bought but still the problem persisted,was driving me nuts,i made one fatal mistake,although i disconnected the switchmode supply from the radio and replaced it with a linear psu i had left it on standby turned on,i went to get a cigarette or if i'm being totally honest i went to build a spliff and while i was doing so i turned the manson switchmode psu off,
all of a sudden the noise on the radio disappeared,despite the fact the switchmode wasn't connected to anything it was still radiating noise,i repeated the experiment with my zetagi switchmode which i'd used for years,it didn't have the popping sound but radios on it had s1 off noise on some channels which i wrongly assumed was my computer which is nearly always on.
surprise surprise s1 off noise showed up on the export radio plugged into the linear psu.turned the zetagi back off,same as the manson,noise all disappeared.
suffice to say i now have only two psu's and both are linear types,infact both are palstar ps15 types and i get zero noise from either on my radios,just like the old days.i will never use a switchmode psu on a radio again.
might not be your problem cominatyalive but may be worth checking for as i know you tried a battery only,but if you didn't turn the switchmode off at the same time it may be the source.
