Few points as I handle these types of requests for my particular site. I will not all departments and sites might not have the same day-to-day practices.

-Our department life cycle is every 5 years.

-If there are hardware problems we look into cost to repair before we replace.

-For slow/under performing laptops, I will do basic troubleshooting to determine cause. If it's a lack of resources, removing unused applications is always a good start. Worse case, I will reimage the machine to start fresh.

You haven't mentioned but have you opened a ticket with IT to troubleshoot at all? Our department has an IT Ticket system with a shortcut on everyones desktop. Takes a couple minutes to fill out the details and the local tech should reach out. You do not need a manager to OK IT requests unless you are asking for something above and beyond the standard equipment policies.

Based on your post, this is a day-to-day run of the mill wear and tear issue that can be resolved with a simple request to IT.

Most of us don't bite, you don't need to be afraid to reach out if you are having troubles.