Bulova chronograph keeps time but second hand and chronograph not working

Yes that's common, most chronograph watch's a small subdial is the times second hand. The large second hand is only for the timing function of the chronograph.

If you haven't got the user instructions you can get them via the following link:-http://www.bulova.com/watches/bulova/marine-star/98b105/

You should see "download user manual" at the bottom of the page.

May be you need to try harder?

I have the exact same issue with the minute hand resting at the 1 minute mark and now I have condensation under the glass. The watch is only 2 months old so I think I will return it.

The problem is in chronograph module or related gear train. To find what exactly the problem is, special tools and equipment is needed as well as watchmakers knowledge and skill. There may be just an underpowered battery, but according to your explanation, I tend to think that the first causes mentioned by me are the right ones. Visit your nearest watch repair shop and ask to check your watch for any faults. Rate me, please.

Your true actual time second hand is on one of your subdials. That big "second" hand is really your chronograph seconds timer. It should start and stop when you depress one of the plungers/ buttons on the side of your watch.
Again, that big hand does not need to be turning all the time (or ever if you never use your advanced stopwatch/ chronograph). The true seconds hand is very small on one of the smaller dials.
Good luck, I hope that's all it is

go to Buliva web site and look for the chorograph 561/598
FEATURES
1. Hours, minutes, seconds and date display.
2. 60 minute Chronograph (CHRONO) with minutes and
seconds display.
3. 24 hour hand, permanently synchronized with the normal
12 hour hand.
A. SETTING THE TIME
1. Pull the crown out to position “3” (See diagram). If the crown has
a “screw-down” lock, then unscrew the crown lock first by turning
the crown toward you, then pull it to position “3”. Do not forget to
screw the crown back “IN” after all setting is completed.
2. Turn the crown towards you (hands moves clockwise) until the
date changes at approximately midnight.
3. Continue turning the hour and minute hands to the correct time.
If it is afternoon you must go past 12 o’clock again (noon) to set
the correct time.
4. When the correct time is set,push crown back to position “1”.
B. SETTING THE DATE
1. Pull crown to position “2”(See proceeding diagram).The watch
will continue to run.
2. Turn the crown away from you until the correct date appears.
3. Once the date is set, push the crown back to position “1”.
Note: Do NOT set the date between the hours of 8:00 PM and
3:00 AM.This would not damage the watch,but the date may need
to be reset later.
C. CHRONOGRAPH (CHRONO) ADJUSTMENT
If the chrongraph second hand is not positioned at the proper
starting position (12 o’clock or “zero” position), use the below
procedure.It does not need to be repeated unless the watch
receives an impact sufficient to move the hand out of position, or
the Battery has been changed.
1. Pull crown out to position “3”.
2. Push button “A” to move the Chrono Second hand (long hand) to
the “0” or 12 o’clock position. Each button push will move the
hand one step – BUT holding the button down will advance the
hand rapidly.
3. Push crown back to position “1”.
D. USING THE CHRONOGRAPH (CHRONO)
Note: The maximum chrono reading is 60 minutes, However the
chrono will continue running once 60 minutes has passed. The
resulting one hour periods may be added together mentally to keep
track of longer periods.
For example – If you know that approximately one hour has
passed since you started the chronograph, and the chrono reads
25 minutes, then you know that the chrono has been running 60
minutes plus 25 minutes, which is one hour and 25 minutes.
1. Push Button “A” to start the chronograph. Push button “A” again
to stop the chronograph.
2. Push button “B” to return the two chronograph hands to the
“Zero” or starting point.
3. The Chronograph can be stopped and started again
(Button “A”), repeatedly, to “ADD” times together.
BOOK NO. 561/598 Chrono FS00/01/10
BOOK NO. 561/598 Chrono FS00/01/10
Watch Setting Guide
4/2007

Try setting the crown to position 2 - i.e. the position normally used to adjust the date.  Then use the top and bottom stopwatch buttons to adjust the minute hand and 1/10th hand respectively.

If you pull out the crown to the 2ed postion the push the upper start button that should move the second hand up to zero then push crown in.

i have the same watch it needs a cleaning by a watch maker not jewler hope this helps