There is a good chance that you will need to open the Wii up and have a look. You will most likely have to realign the drive as there are 2 states that the drive can be in.
1. Loaded: this state is when there is a disk in the drive, there is a bit of metal that physically tried to stop from inserting more then 1 disk.
2. Unloaded: the drive has no disk inside it and can freely accept disks.
Since you removed the disk physically, the drive has not realigned itself to the unloaded state (it's still as if there is a disk in the drive). I would also bet that if you have little kids around that there is something in the drive that shouldn't be there ie. more disks or coins/debris (I see this a lot at my store).
Your original not reading issue may be either because the laser has burned out or could also be related to foreign debris being inserted into the drive. Either way you will have to crack it open, have a look and give it a good test.
To realign the drive, take out the 4 phillips head screws along the top of the drive and the 1 phillips head screw at the bottom left of the drive. The metal cage on the top of the drive should swing open from right to left (there will be a ribbon cable connecting it still on the left). The cage hooks on the right so you will have to push it slightly to the right before it comes free.
With the cage open and sitting on the left you can use your finger to rotate the round bit of plastic with a rubber band on it, if you look at it from the right, you will be rotating this anticlockwise. It will take a few revolutions to realign, you should see the metal prongs at the front of the drive beginning to go down. Once the metal prongs have receded behind the plastic and no longer obstruct disks, reassemble the drive and test it. Also you should have used this time to see if there is anything in the drive and remove it.
Goodluck in your repair endeavors :)