Why is my SN74LS08N overheating?
First... Disconnect everything but power and ground. Make sure power's on pin 14 and ground is on pin 7. Power it with 5V. Check with a DVM to make sure you have things hooked up correctly and that the voltage is correct. The chip should not heat up. If it does, try a different chip- the original one may have been fried. 

Once you have a nicely quiescent, powered up chip that doesn't try to immolate itself you can start adding logic inputs and looking at the outputs. Make sure that the inputs are within data sheet spec (DVM again, at least for the DC levels- scope is better). Once you see the outputs from the AND gates acting like they should, hook them up to the next stage. 

The key to troubleshooting these kind of problems is to break them down to their essentials and add stages only after what you start with is working properly.