stefbv, syphilis, Anne and AM: Thank you for you time and interest. Your posts helped a lot.

Here is how I got it solved: although CPANPLUS version was not that far back-dated, I decided to try to update it to the latest (0.9136). It's not simple to update it, so I used this incantation:

cpan -fi BINGOS/CPANPLUS-0.9136.tar.gz

as Khen1950fx suggested here: perlmonks.org/?node_id=1031040.
This got installed with no problems; I then went: cpanp (invoked CPANPLUS) and entered: i DateTime. It asked me about required dependencies, I answered [3] (Yes to all).

Turned out that wasn't such a good decision, since it got stuck for more than an hour in trying to install DateTime::TimeZone.
I noticed it was eating up 13% of joint cpu power ( which is quite a lot - the PC is quite powerful, 8-core i7 processor).

I Googled a bit and realized it got into a "required dependency loop". I killed the perl.exe process (had to, since it ignored Ctrl-C), and installed the required dependencies manually.

So all looks fine right now.

Many thanks to all who chipped-in for help - Helen

NB for the benefit of the PerlMonks community: some "lessons learned":

1. It is possible (and documented) to run several Perl installations on your system. You have to manage the PATH carefully though (either manually or, if you have Citrus Perl, using the citrusvars.bat utility)
2. CPANPLUS works fine in a multi-installation environment - in fact, it's by design. It creates a "module archive tree" with entries for each Perl version it finds.