can connecting and disconnecting a battery, for over a year, damage any electrical parts?

i've had my durango stored for 1,ahalf yrs, i disconnect the battery, but
connect it, once a month, and its always fired up, no problem,once i ran
outta gas, put some in, a little start fluid, bam, starts up just fine. last time i
tried to start it , no luck. so i go and put about 4 gallons in it, still no start.
we listened for the pump, when i turn on the key. hear nothing.i can
remove gas cap which releases the pressure, try again, no pump. to check
relay,which terminals can i jump, to check relay? or take  a meter and
check the relay by,how?  i get a code PO505, and the fuze , its a square
fuze, not too familiar, with them ,i was going to switch it with another, but its
the only 10 amp fuze. can i set my meter to ohms? i think to check fuze?
connecting, and disconnecting battery, for that amount of time, can it
damage relays, or fuzes, etc, etc...? any, tips, suggestions? any feedback
will be appreciated..a pre-thank you to all....charles92154