Difficulties programming Arduino uno for 24 hour cycle
On the Uno unsigned int is a 16 bit number. That means, that it can hold values between (and including) 0 and 65535. If you try to write a bigger value to this variable, it will cut of the higher bits, so that the rest fits into 16 bits. That gives you a totally different value, which is significantly small than 24h.

The solution is to use a bigger variable type for totalTime.
 You can use unsigned long, which has 32 bits and can hold way bigger values ( 0 to 4,294,967,295 (2^32 - 1)). That should be plenty enough for all your cases.