Sorry, I re-read your email and you do not have a kegging system.  The times I have drank barley wine it was not very or carbonated at all.   Before I had my kegging system and botteled I had a few batches that did not carbonate and in the end most of it got dumped.   I can't drink non-carbonated beer.  I would follow Mr Paul Illa idea, check your temp to make sure it is warm enough but not too warm, every yeast has its sweet spot and then un-cap and put in a very small amount of dry yeast and then re-cap.  Try to minimize the contact with the oxygen and try a few bottles first to see if it works and watch out for bottle bombs..... 

Dipak,

If you have a 5 gallon carboy set up with a C02 tank you could carbonate your barley wine that way.  Take a clean and sanitized keg and pour the barley in the wine quickly minimizing the contact with the air (oxygen).  Close up keg and hook up the co2 and make sure you purge the oxygen out of the keg really good.  Then force carbonate the barley wine.  My technique to carbonate a carboy keg is to crank up the psi to 30psi and top it off every few days for a week.  You will see the pressure drop when the barley wine adsorbs the C02.  You could do a force carbonate faster but after a week I then pull the pressure pin down to 8 to 10psi for serving.

Tom

I bottled some Barleywine about 6 weeks back and it still has not carbonated.  I did add some priming sugar, but have noticed there is absolutely no yeast sediment at the bottom of the bottle.