Hi All, newbie to the forum and hoping for some advice. NB MK2 2001 1.8 VVT not working

Symptoms: Initially it was surging and splattering like it was either starving for fuel or at one stage I thought maybe battery/power - we thought maybe dirty fuel so replaced filer and pump.
Then all of a sudden it was running rough at idle, take off and well, all over the range and felt like I was running on 2cylinders, especially in higher rev range. VVT not kicking in at all. Plugs were black full of carbon.

So we replaced the following and still not kicking in:
Spark plugs
O2 sensor
Maf sensor
Temp sensor
Coil packs
Injectors
Cleaned vvti solenoid

This has helped in lower rev ranges however we have replaced the plugs now twice as the new ones got dirty also... Less than 100k's.

Next step: cleaning/detergent oil

Questions:
1. Does VVT require power? Before this happening, noticed battery was getting weaker... Maybe alternator?
2. What else? Any ideas what to think of next?

Thanks in advance!