New ask Hacker News story: How do I check if our home network is compromised?

How do I check if our home network is compromised?
3 by slategruen | 4 comments on Hacker News.
We have been experiencing regular network slowdowns and packet losses at around the same time for the past few days. It usually happens in the morning even though our network usage is not as heavy as it is at night during that time. The slowdown is not limited to a single device so it had me kind of worried about the security of our network. I have not contacted my ISP about this issue because I want to rule out any fault on my side. However, one problem I have is our router's software is proprietary and the network device given to us is a modem/router combo. I have administrator access to the router but that's about it; flashing it is probably out of the question. Any suggestions how would I deal with this? Where should I start troubleshooting?