When you put it outside, the sun is not able to hit it, is it?The light-colored leaves look awfully bleached. Sun will burn an indoor plant just as quickly as it will burn a person who has never been outside. The corn plant will be perfectly happy to stay indoors; a spot where there's enough light for you to read a book will be enough light for the corn plant. Also, 'canes' don't like to sit in wet soil. Yours has a very small root system; allow the soil to aerate to the point that if you pinch soil from half way down the pot, it will feel almost dry, barely sticking together. Then you can water it enough for a runoff from the drainage holes. You can cut off the brown leaves flush with the stem, and trim the brown tips nicely, with scissors, so that the original shape of the leaf is maintained.

Hi & welcome to Gardenweb.

Good advice, I support every word. Don't think this plant needs fertilizer at the moment because I suspect the roots may be damaged and unable to property utilize it. It sounds like this plant has been in the same soil for a long time. Have you repotted it before? I took some pics when recently repotting my Mom's corn plant. Compare your plants' roots and see if you think they may need attention. If you see the compaction, circling, or find mushy or discolored roots, the repot would probably be helpful.

Here is a link that might be useful: Corn plant repot