If a resolver tries to send its recursive DNS queries to a server that refuses those queries, or the queries time out, then the resolver was originally supposed to try to do an iterative query itself: ask the roots, follow referrals until an error is detected or an answer is seen. However, nearly all resolvers are stub resolvers and simply choke at this point: they rely on being pointed to a short list of DNS servers where they can send recursive queries, and don't support doing iterative queries. Moreover, some networks only allow DNS queries to go to a small list of approved DNS servers providing recursive service. In this case iterative resolution wouldn't help.
(As Martin Berger points out, if the DNS server where a recursive query is sent happens to have the answer in its cache, and it is prepared to handle the recursive query, then it will supply the answer from its cache. Presumably your phrase "if there is no recursive querying" rules this out.)
The root servers answer recursive queries with referrals to other servers. This usually does not answer the query, and further queries are required.
If the DNS servers to which the resolver sends queries are not reachable, a DHCP lease refresh may provide a new list of servers and fix the problem.
A packet capture tool like Wireshark can show the DNS queries generated by your machine and the answers it receives.
For completeness, this is how the DNS works.
Usually the resolver is set up as a stub resolver, to send all DNS queries to a server. This is often done by including the IP address of this server in the DHCP negotiation when connecting to the network. The server's IP address can also be in
/etc/resolv.conf or some equivalent configuration entry. When a DNS server sees a recursive query, and it is willing to provide an answer to that recursive query, then it usually does iterative resolution.
Iterative resolution works by sending the query to the servers for the root domain. This is a list of servers that changes infrequently; the latest one is available by FTP.
Queries to the servers for the root domain result in a referral, giving a list of name servers that are more likely to be able to answer. The resolver picks one of these, and sends the query there. This continues until it receives an answer, or something goes wrong: a loop occurs, a server responds with "NXDOMAIN" (no such entry exists in the DNS), or the query times out.
Name servers also keep a cache of previously seen name servers. When a DNS server is started, the first query works as above, but subsequent iterative queries will use the cache to short-circuit the process and will be sent directly to the best server, if one is known.
Instead of the term "recursive server", it is more correct to refer to a DNS server being prepared to answer recursive queries. Many DNS servers are prepared to answer recursive queries for some "trusted" clients but not for the Internet as a whole.