Toggle LED on when Button is pressed PIC
Your problem is probably caused by the analogue module. According to page 84 of the data sheet you linked the ADCON1 register needs to be set correctly to enable digital functions on PORTA.

A value of 0b111 is likely to make your code work (but see other answers about debouncing). Various other combinations of values are available in the table for REGISTER 11-2:



This type of configuration is common on the smaller 12F and 16F devices, which lack the ability to individually select analogue or digital per-pin.

As Spehro notes in the comments there are a number of ways to find which registers are associated with a port.  The easiest is TABLE 4-2: SUMMARY OF REGISTERS ASSOCIATED WITH PORTA, which looks like this:



This table becomes even more useful on large devices that have lots of functions such as extended analog features or capture and compare.  Many of these need to be disabled after reset (e.g. comparators) and some might interfere unintentionally if misconfigured (e.g. MSSP).

Note that this table also shows that the 16LF76 does not have LATx registers, so other comments above can be safely ignored for this device.