StarLord likely jury rigged a power source to keep his Walkman playing:

http://filmschoolrejects.com/features/guardians-of-the-galaxy-awesome-mix-survived.php

I bolded the relevant passage in this reblog:

As a child of the 80s, I am intimately familiar with cassettes, Walkmans, old-school 1/8” headphones, and the awesomeness of a mix tape. However, I also remember burning through my fair share of cassettes in my youth (and needing a pencil more than a few times). Of course, the track list for “Awesome Mix Vol. 1” will always be awesome, but seeing all that Quill goes through in Guardians of the Galaxy, it got me thinking. Would that mix tape have lasted for 26 years in space? Would it even still work?

The Answer: Yes, but playing it might be a bigger challenge.

Sure, you had to rewind and fast-forward through tapes to get to certain spots, and you can’t jump around instantly like you can with digital media, but cassette tapes offered a flexibility and functionality in their heyday. Not only were personal portable tape players like the classic Sony Walkman extremely stable (unlike their CD counterparts that tended to skip when jolted), the tapes allowed for even the least-technically-minded person to make a mix. All you needed were two tape decks and the right cable.

However, one of the drawbacks of mix tapes was their lack of longevity. On the positive side, the cassettes themselves were strong, and it took a lot to damage them. As long as you were somewhat careful with your equipment, it was unlikely your tapes were going to be eaten by a player – and if they were, you could literally splice them together back home.

However, making a mix tape on a 60-minute Maxell consumer grade cassette was never going to come off with the quality of studio masters or even the original store-bought product. There was relatively little quality lost when they were dubbed once, but after that tape was played over and over again, damage would occur. The tape could be stretched out. The heads that read the tape could affect the magnetic encoding on the tape itself. Worst of all, leaving your tape in the car where it could get too hot or too cold could damage the recording.

When it comes to Peter Quill’s “Awesome Mix Vol. 1,” it was his only copy. He could have made dubs from the original master, but as is seen in the film, he doesn’t. He plays the hell out of that tape, both in his deck on his ship and on his Walkman. Because audio tapes can last anywhere from 30 to 100 years if cared for properly, he could have kept the tape in decent condition.

But that was just the tape.

What about his equipment?

Here’s where Quill might run into problems. Because he was stranded in space as a young teenager, he couldn’t just run down to Radio Shack to pick up a new Walkman whenever he wanted one. If your interest is to preserve a recording system in space, that’s one thing. However, if you have only one or two playback machines and a single mix tape, things get a lot dicier.

To keep a tape player functioning properly for years, he would have to have some way to perform maintenance on it. At the very least, it would be good to clean the heads of the system at least a few times while on his journeys. Of course, he could presumably figure out a way to do this with whatever resources he had access to in space.

Then there’s the power. The tape deck in his ship was certainly wired into his vehicle’s electric system. However, his Walkman was not. Anyone who used portable tape devices knows that those things go through batteries like crazy. According to Radio Shack, a typical portable tape player will run for about 18 hours of continuous play before the AA batteries wear out. That’s not a big deal if there’s a ready supply of AA batteries at every supermarket, gas station and electronics store within a mile or two. However, Duracell doesn’t have much presence off our planet.

Unless Quill found a way to jury rig a portable power source for his Walkman (which is quite possible), he would probably need a couple thousand AA batteries to keep it running for 26 years.

Still, this is a better option than if his mother had put the “Awesome Mix Vol. 1” on a CD or an iPod. With the physical durability of a cassette tape, he wouldn’t have to worry about the CD (which is also prone to deterioration over time) skipping in the middle of a song or have to forever search for a USB port in which to charge his iPod.

However, while it is possible for the tape to survive and the equipment to run, there’s still a greater challenge to playing “Awesome Mix Vol. 1” for 26 years.

Would it play in space?

Space is a hostile environment. While it is a whole lot of nothing, the scant few things found in its vacuum can wreak havoc on electronics. The first problem with anything in space is that it is exposed to extreme temperatures. The ideal temperature in which to store a cassette tape is between 50 and 70 degrees Fahrenheit. Unfortunately, the temperature in space can fluctuate to wild extremes, depending on what it’s exposed to. It can be as low as 455 degrees below zero Fahrenheit in the coldest part of space, but it can also be millions of degrees in the path of a solar flare.

Even if the temperature can be dealt with, there’s other things in space that would cause problems. Because there is no atmosphere to act as a cosmic filter, space is filled with high levels of radiation, which can cause a wide variety of problems in electronics. The smaller the electronics, the greater chance they will be susceptible to radiation that can cause electric arcing, voltage spikes, electronic noise and many other issues.

It is because of this intense background radiation that electronics built for space exploration are shielded or radiation hardened to counteract the effects. Because portable cassette players have been made specifically for terrestrial use, they aren’t made with radiation shielding.

So, if Peter Quill took really good care of “Awesome Mix Vol. 1,” and if he managed to keep his equipment in working order with a proper power source, and if he kept the tape in proper storage without exposing it to extreme heat or extreme cold, and if he only used his Walkman inside a space ship or on a planet with a thick enough atmosphere to filter out ionization radiation, then he could still be hooked on a feeling 26 years later.

So it IS possible he could still be playing the walkman 26 years later.

Seems legit.

Not to mention that magnetic tape stretches, decays and loses it's actual magnetic encoding information over time.  No tape lasts for 26 years of frequent usage.  Each rewind literally degrades the sound quality.

Good point.

I was disappointed not to see one of those double-tape decks somewhere on the ship, where he could keep making copies of the original and not wear that out.

But that would be my guess, that he has a casette-to-casette deck somewhere on the ship.