I'm sorry to hear this. No one should have to go through this: an update from Apple resulting in unuseable hardware.
Today I searched again and found this link written recently:
http://techland.time.com/2013/06/06/apples-ios-6-1-3-update-can-knock-out-wi-fi- bluetooth-and-cost-you-200-to-fix/
If we search for "iphone wifi gray" or "iphone wifi grey" we would get a long list of different methods people used. This is unbelievable, because one of the reason for getting an iphone in the first place is a phone that just works. Now look what people would have to go through!
If enough iphone4s who are still under warranty go to Apple to get this problem fixed, maybe, just maybe, Apple might offer a free fix for people out of warranty but got hit by their "upgrade".
After all, it isn't your fault that you upgraded. Appled wanted people to upgrade for the latest security plugs.
Some folks cleared the problem by simply putting phone in airplane mode, reset, then take out of airplane mode. One guy cleared it by removing "forgetting" a bluetooth device.
Please read this one: http://transfer-iphone-contacts.blogspot.com/2013/07/iphone-wifi-greyed-out.html
This article above gives you the steps for a fix that works for some people. In fact, it's the same method that the fix on apple's support site: http://support.apple.com/kb/TS1559
Here is another similar article: http://www.appledystopia.com/tech-tips/ios/fix-grayed-out-iphone-wifi/
I would hold off on the blow dryer method given below unless you have no other options left.
As weird as it sounds, people have been putting their iphone4s into the freezer, some have tried blowing hot air directly onto the chip: http://www.ifixit.com/Answers/View/135053/WiFi+Greyed+out+iOS+6.1.3
Summary:
Ways to "fix" wifi grayed out problem on iphone4s after upgrade to 6.1.3:
1.) Easy one - wait for ios7 is out, upgrade and see if the wifi being disabled can be cleared. This would only work if the wifi chip itself or the soldering isn't damaged, ie the chip is "stuck" in a disabled state. A major upgrade might clear it.
2.) Use the put-in-airplane-mode-reset-phone trick as described by Apple and some of the articles.
3.) Get a quote for a repair (not a $200 replacement - one can get a new iphone5s for that kind of money).
4.) If you have another back up smartphone that can carry the day, and this iphone4s is expendable, and you don't want to pay money for repair, you might want to try the more adventurous blow dry method.
(But I wonder, if the wifi chip got disabled by overheating, how's more heat going to fix it? Is this method going to actually "melt" the soder so it reconnects after it cools off? It's risky, one would do it at one's own risk)