I would probably replace it.

Probably not what you want to hear, but you would be better off replacing it if you need the extra refrigerator space. New models are much more energy efficient. Check out clearance and "bruised" models. You might be able to find a good deal on a new one. Also check with your local electric company, in our area they offer a small rebate and free pickup if we replace old models with more energy efficient ones. Good luck.

I would replace it. 10+ years is pretty old for an appliance these days.

I'd probably replace it too depending on how much the repair would cost. But I will say that we have a 1997 basic Kenmore/Whirlpool top freezer that we intended to replace when we remodeled our kitchen three years ago. We kept it because we couldn't make up our minds on which new model to get (and wanted to postpone the cost--turned out to be the perfect decision, because the almost-what-we-wanted model we were planning to buy was just updated this summer to be exactly-what-we-wanted!) That thing is still going strong, and we used a Kill-o-Watt to measure its energy use and were surprised to see that it is actually competitive with what we'd be replacing it with (though we will be going to a slightly larger refrigerator, which accounts for some of that difference). So that's just to say--you might well get a number of years out of it yet if it's a cheap fix, and it might not be the energy hog you think it is, depending on the model. (You can actually look this up for many models in the link below; most refrigerators will also become less efficient as they age, though surprisingly our readings were on par with the original readings for our model.) It may be worth at least getting an estimate on the repair.

Here is a link that might be useful: Energy Use by Model

Note that Salvation Army doesn't accept appliances over 10 years old as donations. That would make me tend to say replace it.

First, I'd check the obvious stuff.

When you plug the refrig in, does the compressor kick on?

Have you cleaned the coils?

Does the fan that cools the coils kick on?

If the refrig needs to be replaced, what I would do is look for an older Kenmore/ Whirlpool. There are lots of them floating around and, in my area, can be had for $50-$150. (Craigslist, garage sales, estate sales, etc.) Esp. since it's the basement refrig where it probably gets opened 2-3 times a week vs 30 times a day. Basements are usually cool anyway and less frequent use means it doesn't have to recover from dumped refrigerated area nearly so often as a kitchen refrigerator. Less recovery = less energy used.

I have a 30 something YO Kenmore in the basement and it keeps ticking along. It's only needed a couple of repairs...an ice maker motor and a new defrost heater. Oh, and I replaced the door sealing gaskets once. Easy DIY repairs; I fixed 'em myself. I'm actually afraid to replace it with a 'new' appliance since I figure there's a good chance the old one will still be running when it's replacement has gone belly-up.

I have an even older Kenmore chest freezer that is still running and has never needed any repair.

I just repaired my almost 10 year old fridge. Some type of switch for the compressor died, it was less than $200 to fix.

Try to figure out its problem to see if repairable
If not, check with your utility company to see if they will pay you to take it away and then get a newbie.

You can easily buy a basic fridge a few years old on craigslist for $200 or sears outlet refurbished, or a new one for about $400 so it is is not easy to repair I would choose that route. Just ask them to have it plugged in and cooling when you go unless it is warranited, and buy an instant read thermometer to take with you to check the cooling temperature. Your energy savings may be upwards of $10/month with an almost new fridge.

My utility company will not take away a fridge that does not cook. You should check with your own.