Is dealing with checks and depositing their value into a current account in a usurious bank permissible or forbidden, given the unavailability of Islamic banks?

It is not permissible to deposit money in interest-based banks, as this constitutes cooperation in sin, except in cases of necessity, such as the absence of an Islamic bank and fear for one's money, or the need to deal with entities that only accept checks from interest-based banks. In these situations, deposits should only be made into current accounts. If you are not compelled to deal with the company in that manner, then it is not permissible for you to open an account in an interest-based bank.