If your kid's R4i cart not yet have WAIO or YSMEMU/TTMENU as their secondary firmware, try installing one.
Try adding WAIO.NDS from : http://forum.romulation.net/index.php?topic=39701.0
Its the easiest to install as its only basic Drag and Drop method. Download the file from Coolkill3r with the name WAIO for R4 Clones. Cause your kid's cart are R4i which is a clone version of the original R4.
There's the tutorial when you click SPOILER below it. Simply follow how to install it and it should temporarily fix your issue. You might want to keep the link to it for later, since this firmware get updated each time new games are released.
Other than that, you might need to also upgrade your kid's cart with the latest kernel version for R4i, you can find it here: http://www.linfoxdomain.com/nintendo/ds/
Follow the instructions on how to install it.
I won't recommend trying to install YSMENU since its a bit tricky for parents unless someone in this forum willing to provide you with a package of his/her entire latest kernel and firware copy. I can't provide you with one cause I'm using the original R4 version.
Also I should bring forward to your knowledge that most game roms this days requires some patching, so you might want to look around for it too according to what your kids are playing at the moment. Patches available here are mostly in the form of xDelta or Rudolph versions. If you don't understand how to do the patching, best is you look around for someone who had uploaded a game rom marked as 'pre-patched'. In here, members who usually upload such pre-patched games are Kiekoes, Totallydood, Halo-101, Zaetrix, Solnano, Coolkill3r, and a few random members. But those are the season members who host such files.
Post Merge: [time]1288279177[/time]Replying to #3
It could also mean your kid's cart had a missing file. I experience such issue before on my other cart which is a firelink cart. I simply upgrade it with the latest kernel version from linfoxdomain. Maybe your kid had accidentally deleted something without realising it.
But it would be safe to try install WAIO first and see if it solve your problem. You need to also have a WINRAR or 7zip to extract those files. You can download a free 7zip version in the net, or use a trial ware for WINRAR.
If you decide to try upgrading the cart, remember to duplicate it into your computer first, just in case things go wrong. Might want to ask your kins or friend's kids who know about this, as its rather tricky.