System Interrupts 35% CPU usage in safe mode HP Pavilion dm4 64bit

At wits end.
My laptop is so slow it is almost unusable. CPU usage is 30-40% constantly, even in safe mode with practically everything disabled. All caused by System INterrupts.

I have cleaned out an unused software and datafiles, removed AVG (relying on Windows Security Essentials and Defender with Malware Bytes uploaded and run weekly then uninstalled). I have defragged and run full virus/security checks.
We have tried disabling drivers one by one and using latency monitoring programme suggested elsewhere on the forum, but nothing makes any difference. The latency spikes are irregular and in amber but not going into the red.
Laptop overheats seriously, and I only get 1hour out of NEW HP battery (problem started before battery was replaced but we have checked the driver for this). One USB port has stopped working entirely after being a bit dodgy but I again disabled drivers and no improvement.
Keyboard also seems to miss characters regularly which looks to me like it is due to slow reaction

Can anyone suggest anything I haven't tried, or do you think this is a hardware problem and it needs to go to a clinic? I suppose I could always buy a new machine.

Thanks

OK maybe we should have done this first.

I removed the battery and the CPU usage fell massively but was still spiking to using 35% of CPU frequently.
A bit more detective work and more searching online threw up issues with HP wireless assistant.
We updated the HP update - this did not update my old version of HPWA, so we downloaded v 40.0.10 (impossible to find on the HP website but we did find it on another site for free) just in case we needed it - ie in case the wireless button stopped working when we disabled HPWA.

THEN disabled the old HPWA - no problem with wireless button or internet access so have not installed the newer version. This fixed the spiking of CPU and my keyboard works fine (haven't yet checked the USB port).

THEN I experimented with putting the battery back.

Miraculously, CPU usage is down to background 0% and the fan has stopped whirring away continuously.
I am now experimenting to see if battery lasts longer then 1 hour this time.