Engine valve noise

I was looking for some help with my car 2003 Daihatsu Sirion ( a Toyota) and wanted to ask you a specific question - I've described the problem below and was hoping if you could help me:
I had valve noise ( I could hear it from the top, as well as it slowly disappeared when the car was getting warm) and I decided to change the oil because I thought it was getting too tick (no idea what was the original oil, but I drove the car for at least a year and a half without any problems, going through the previous winter but this winter, the moment it started getting cold the valves started knocking).
However, after I changed the oil on my Daihatsu Sirion ( a Toyota) with a new fully synthetic 0W-40 (Mobile) the problem was still there. And it seemed as the problem was to a lesser extent (like the oil was getting up faster at the beginning). But when I left the car in the garage without driving for 2 days and afterwords I tried to start it, it was a mess: everything shaking, hard to start, valves clunking like never before and etc- which was probably due to the oil being down and it took a minute until it calmed down a bit, but the noise was still even worse than before. Again I let it warm up for 20-30 minutes, and it was ok I guess.
The engine on that Daihatsu is a small 1.0L DOHC and I thought that thinner oil would be better for the winter. Do you think a thicker oil would help (the old oil was thick, but still could hear the valves knocking and it wasn't doing that the previous winter). Can't figure out what to do exactly and how to troubleshoot.
Any help would be appreciated.

Sincerely,

Ivan

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