Sorry for replying not sooner, pfloyd1 and Arachne.
I have been using other software; not just Alcohol 120%. It has made no difference.
In terms of getting new and different brand DVD+RW discs, which I did, it has not made any difference. I have got some brand new Verbatim as you, Arachne, have suggested .
Just to re-illustrate my current situation, I could write DVD-ROM discs but not DVD+RE discs. This just happened in the last couple of days. I used to be able re-write DVD+RW but now when I try it says the discs are DVD-ROM instead and it asks me to use different type of discs. I wonder whether it is to do with me flashing my drive with firmware. I have only always use the right firmware, obtained from http://rpc1.org/.