3 year old hen laying around-how do I figure out what is going on?

If she is walking slowly?  Walks as is there is pain in her lower innards as she walks?  If she look swelled up and larger than normal?  If she seems to avoid the other birds, as if she is hiding the fact that she isn't well, something chickens are expert at doing?  You need to take a few steps.

I'd give her a warm soak in a tub of tepid to warm water.  She if this relaxes her and perhaps she may pass an egg.  Don't be in a rush to take her out of the warm bath.

See how this goes, but all too often, this doesn't end well.

Blowing her dry isn't too important, if your weather is typical summer time in North America.  She'll dry pretty quickly all by herself.

The sitting around, the slow walk is troubling.  Again, this is important.  Does she seem swelled or heavier looking than normal?  Especially does her lower abdomen look filled or swelled?  The hen on the left of my photo below?  Within days of taking this photo, she began to go into a steep decline.  Now, I can look back and see the swelling in this photo.  She waddled about, didn't do much other than lay around.  Two warm baths and vent inspection proved futile, I'm sad to say.  I gave her every chance, but had to eventually put her down.  She was suffering and filling with fluid.   I'm just trying to gently prepare you for the worst.  Here's to hoping it doesn't come to this.

i hope your chicken is ok - Fred's Hens' advice is extremely helpful with the picture of a sick hen. 

You could also feel her abdomen and see if she has a bloated abdomen.  If she does, you need to take immediate action - i think in this forum, there are several threads discussing about the possibility of egg peritonitis, egg bound, etc.  And like Fred's Hens' said, if your hen has fluid, that's a concern.  

In all honesty, will you be able to get your sick hen to a local vet, who is a poultry qualified vet to see your chicken?  I maybe over-react here, but the way you described your hen, I'm afraid you really need to take immediate action or it maybe too late.  One thing is for sure, she has serious problem that you need to help her.  I'm really sorry, but keep us up-to-date.  I sure hope I am wrong...