Mine does this as well. To fix it, I run an Epson cleaning sheet through the printer a few times and it starts working again. Unfortunately, this is only a temp fix and the problem will return after a few prints.
After having the same issue of passing the paper through, I found there is a maintenance setting (WF-3620) to clean the paper sensor and the roller. I did both and have progressed to cleaning the heads. I purchased the printer from Goodwill, so I do not have new printer cartridges. However, I now have the confidence to purchase them.