I sincerely doubt this relates to your console being modded. If that were the problem, it would most likely stop the game from loading up in the first place.
It's always possible that there's something wrong with a disc, so if it's only one game doing this then that could be it. That said, if your Wii is in less than stellar shape, then perfectly fine games that use dual-layer discs can be tougher for it to read than the usual single-layer discs.
(EDITS: Also on this note, dual-layer discs can be a lot pickier, malfunctioning due to not-so-visible dust, smears, etc. Not too long ago I specifically had issues with Metroid Other M. Cleaning with an every-day cloth towel did nothing. I tried one of those cloths specifically meant for cleaning LCD screens and that did the trick)
It is possible that there are minor issues with your system. I got a launch Wii and it started acting up within the last year or so, failing to read discs and locking up mid-game. I found two (fixable) issues that you'll probably want to be alert for:
1. Dirt on the lens. If you've had your Wii for a long time, you'll want to invest in a cleaning kit. It's 10 bucks off of Nintendo's website (for some reason other retailers tend to jack up the price). Even in a clean household, 4 or 5 years is plenty of time to collect a fair share of dirt.
2. Overheating. If your Wii gets hot even when not playing games, that's WiiConnect24 taking its toll while the fans aren't running. Again, I have a launch system and this only became an issue within the last year (not sure why), but once it started it was a frequent and frustrating problem. If you go into your Wii's system settings, turning the "Standby Connection" option off will solve the problem. That stops your Wii from connecting to the internet while the system is "off" (the light will be red instead of yellow), but it leaves the actual WiiConnect24 agreement unaffected so that you're not denied access to the Shop Channel and such.
Note that leaving the Standby Connection on and manually "powering off" the Wii by holding in the button until you get a red light may not help. In theory this should stop it from looking for a connection while not playing, but my Wii stayed hot anyway until I turned the Standby Connection off in the system settings.