Update... it's been 2 months since I started this thread, and I have new shoots and some buds on one of the orchids. Thank you for the advice. I think part of it is the location. The one that has started again is sitting in a north-east window, so I will move the other one as well as see what happens.
Now I'm not sure what it means that I got so excited over a houseplant bearing buds. It shows either that I appreciate the small things in life, or my life is so dull in isolation...
I saw the title and thought 'Oh don't talk to me about orchids' I recently had to perform a cull as the kitchen was full of the blooming things (or rather not blooming) I have an enormous cymbidium (sp?) orchid which must be nearly 20 years old, and hasn't shown any sign of flowering again in all of that time. Any ideas please?
Patience is the answer. They will bloom again on new stems if the old, dead (dry and brittle) stems are cut right back to obviously living tissue. I put my cut down plants into a light porch area where they can rest as long as they need. Just occasional watering and checking for pests until a new flower shoot forms. New roots will also grow. I have 3 moth orchids now with new flower stems after 12 to 18 months 'rest'. Good luck, don't despair.
I'll give it a go. Yesterday I loosened the root ball, sprayed them with water and repotted. I also picked up some orchid plant food so we'll see what happens in the next month or so. These are the typical grocery-store orchids received as gifts last year. Phalaenopsis Orchids. They bloomed for ages and I would like to see if I can get them to bloom again. In the meantime they are rather sad looking.