SQL Server: Effect of Setting These Index Options
The article linked to in the comments makes it clear, but let's prove it with an example.

CREATE TABLE t1(a int);
INSERT INTO t1(a) VALUES (1), (2), (3), (4), (5), (6), (7), (8), (9);

CREATE CLUSTERED INDEX IX_t1
    ON t1(a)
        WITH(ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON); /* Default */


BEGIN TRANSACTION;

    UPDATE t1
        SET a = 10
        WHERE a = 1;

    EXEC sp_lock;

ROLLBACK;

DROP TABLE t1;


Results (filtered to SPID and table of interest):

spid   dbid    ObjId       IndId   Type    Resource        Mode    Status
52      6       213575799   1       PAG     1:118           IX      GRANT
52      6       213575799   1       KEY     (de42f79bc795)   X      GRANT
52      6       213575799   1       KEY     (241332e1ddb0)   X      GRANT
52      6       213575799   0       TAB                     IX      GRANT &lt;--
52      6       0           0       DB                       S      GRANT

(There are two KEY locks because SQL Server needs to protect both the "before" and "after" index values. If you want to see this, run SELECT a, %%lockres%% FROM t1 before and after the UPDATE statement.)

If I run the same script again with the clustered index definition having ALLOW_ROW_LOCKS = OFF and ALLOW_PAGE_LOCKS = OFF, I get this:

spid   dbid         ObjId   IndId  Type    Resource    Mode    Status
52      6               0       0   DB                    S     GRANT
52      6       229575856       0   TAB                   X     GRANT &lt;--

So it should be pretty obvious now why you suddenly started having deadlocks!