Проверка подключения к сети. Проверка сетевого подключения.
Проверка соединения с сетью. Проверка сетевого соединения.
Notes:
1. Проверка is a noun. It is proper translation of the gerund 'checking'. In the constructions where your program IS checking something a verb should be used: "программа проверяет подключение" (program is checking...) .... "проверяется подключение" (passive: connection is being checked)
2. Соединение is the proper translation of 'connection' (and is arguably a better Russian).
Пoдключение was used to denote the process of 'connecting up' - but in recent decade(s) "подключение к сети" was used in some products (at least in MS Windows) to translate 'network connection'.
In the context of checking the quality of connection I'd say соединение is better.
If your application tries to determine whether the device is connected, both fit.
Both terms are perfectly recognizable.
3. google
проверка "подключния к сети" 1 900k
проверка "соедиения с сетью" 170k
проверка "сетевого подключения" 59k
проверка "сетевого соединения" 38k