Pushed commits into repo, but repo on server contains no files
The server only contains a bare repository, i.e. no checkout. The files are only stored in the objetcs/ directory and the pack files you mention. What you can do to verify that the files are indeed there, is e.g. to create a new clone from the server on your local machine. Alternatively, on the server, you can do a
git ls-tree -r masterwhich should give you a list of all the files along with their mode and hashes.
EDIT: You'll want to read the chapter about Git on the server in the Pro Git book.