Open it up and see if any of the capacitors are leaking! Soldering is a great skill to learn and you can fix it yourself.
The biggest problem people have is buying a bad soldering iron that gets way too hot. You can get an excellent iron for only 10 or 20 dollars more than the garbage out there. I used to recommend the TS-100, because that's what I use and love, and they used to be way cheaper. The TS-80 was an upgrade to that, which was also nice but I never liked. If you've got the money, I still recommend them. However for the budget minded, the pinecil is almost the exact same thing, it's well made, and it's still like $30-40 bucks. In fact some people prefer it over the others. You can power it with a beefy USB-C charger if you have one, or an old laptop charger if you want to cut up the end and put a barrel jack on it. The thing pulls about 90 watts at full tilt, but only for brief periods.
Next you want to buy yourself some practice boards, you can get soldering kits from AliExpress that will let you build little flashing trees and hearts and stuff. Or even small handheld games if you're getting better at soldering.
Then you watch YouTube tutorials, find several. You want to focus on quick work, at low ish temps like 280C, keep the tip clean, and flux is your friend. The very tippy tip of your iron should always be shiny, if it starts turning black, it's building oxides from being too hot and not enough flux. Clean that thing with flux. If you leave it that way too long you'll ruin it, that's why most people struggle to solder.
Then once you've learned, and you're ready to go. Watch YouTube videos on fixing the Xbox, buy the caps, crack that thing open and have fun. Caps aren't that hard to replace, compared to other soldering projects. You'll do fine 👍
Hey thanks. I may need to solder something in the near future, and it's always felt a bit daunting to start/learn for some reason. This comment was super helpful.
I bought a cheap learn to solder kit and did that project before fixing an old Dell motherboard. It came with a soldering iron but agree with the poster above that a better soldering iron makes a big difference.