My computer monitor's power brick (12v and 4.16A) went bad. Can I use a power brick that has output 16v and 3.75A? The input values are the same.
I doubt that it would work, and it would be very risky. The best thing that could happen is that nothing will happen and the monitor will just stay off. However, because the voltage is higher, it actually could damage the monitor. I wouldn't try it.
Higher current (A) is okay because the device won’t use as much, but higher voltage (V) is going to “fry” it.
Conversely, lower voltage is unlikely to cause damage since the device simply won’t have enough power, but lower current can cause trouble because the power supply cannot provide enough.
In your case, the “replacement” power-adapter is both higher voltage and lower current. In other words, it won’t work and at best will do nothing, but in all likelihood (especially if the monitor is not a super, high-end brand) will likely damage your monitor.
Look around for another one (with a compatible connector) that is equal to 12V and at least 4.16A).