The ballast could be the issue.

What kind of CFL? Replace vs. rehab depends on how much time you have. You can replace the ballast and lamp with like. You can also replace the ballast, lamp and socket with something more modern if you want to fiddle with your favorite lamp.

Most of the florescent lamps that I've had, over the years, failed just exactly as yours did. They would take longer and longer to come on, and those I had in the garage might not come on if it was cold. Replacing ONLY the florescent tubes, has always fixed the problem, so I would try that first.

Gary

Yes, that seems to be the standard way to trouble-shoot that kind of problem as opposed to a sudden failure.

1)replace starter if there is one (rare these days)
2)if starter replacement does not work, replace lamp
3))if lamp and starter replacement does not work, replace ballast

The trouble with this is that some of the older systems have lamps that have become very expensive. I have a bunch of ancient preheat luminaires under the cabinets in my kitchen. A bad ballast or starter can take out a lamp in short order and the lamps are about $7. I've stopped working on them and I plan to replace them when I get the time.

In the OP's case, I think that the older two-pin CFL ballasts and bulbs are rapidly becoming obsolete. It might be better to upgrade the luminaire to a 4-pin socket, ballast and lamp if the lamp is good quality and loved providing the owner is handy and has the time.

I just got a new lamp (it's a 2-pin gx23 base lamp). I was able to easily remove the old one, but getting the new one in is another story. I don't want to risk a broken tube, but cannot get the lamp into its socket! Any tips on that?

"cannot get the lamp into its socket!"

Are you sure it is the correct lamp?

The manufacturers used to use different bases to prevent the wrong lamp form being installed in the wrong fixture (and thus not correctly matching the ballast).

Little things like plastic tabs on different positions on lamps that otherwise appeared identical.

I am positive it's the correct lamp. Everything lines up,and it looks exactly like the one I removed (different brand, but otherwise identical).

Try putting the old lamp back in a time or 2, and see if it goes back in easy, that way you don't break your new light, and you will now whether the problem is the fixture or the new light.

Gary

I will try that,though it may also be that the old one is "broken in" or loosened from getting it in. We think it was hard to get inserted last time we had to change it, too, though it's been so many years, we don't recall how we finally solved it!

Hold old and new side by side as they would instal and look at the pins and all the plastic tabs that are there.

I did it! After putting the old one in and out, and looking very carefully, I noticed that both pins were smooth on one side, a bit indented on the other. After looking at the new one, (not exactly the same, since one pin is indented on both sides), I worked carefully to align the pins with the holes, with the lamp facing the same direction as the old one, and it went in with just a little push. I don't know if the indents actually matter, or I was just being more careful with lining up holes and pins, but at least it worked. (If the indents are, indeed, relevant, they should say so on the package!). Thanks for all the guidance.