In mission 7, it is possible to make the game unwinnable if you divert power to shields before diverting power to weapons first. If you do that, you cannot switch it back and you cannot learn that the weapons are jammed, therefore you cannot continue.
In mission 7, after the Elasi ship appears, it takes 1 minute 40 seconds until you gameover, if you didn't raise your shields.
I found a really useful bug in ship combat:
You can bring up Kirk's menu options (by pressing K) between firing projectiles, and the cooldown will run out while the game is paused like this. This enables you to shoot powerful blue projectiles rapidly and destroy even the Enterprise II in mission 7 quickly.
Here is a step by step solution. I wrote it so that I can understand it. You will need to get familiar with the game yourself in order to understand it.
[Escape]
Lose the battle
[Escape]
MISSION 1 "DEMON WORLD"
N Map --> (19)Pollux
O Orbit planet
K Beam over
(Go north)
Phaser enemies
Pick up hand from floor
(Go south)
(Enter top building)
Use glass container, dialogue option 2, 6
Pick up Metal
Use hand on desk
(Leave, go south)
Use red phaser on rocks (top left first)
Use hand on panel
(Go south)
Use YRB panel, set all to below middle
Use metal on alien
[Escape]
MISSION 2 "HIJACKED"
N Map --> "(15)Beta Myamid"
[Escape]
Win battle
O Orbit planet
H Hail ship
[Escape]
H
[Escape]
H
[Escape]
H
[Escape]
H
[Escape]
H
[Escape]
MISSION 3 "LOVE'S LABOUR JEOPARDIZED"
[Escape]
N Map --> "(3)ARK-7"
[Escape]
Win battle
[Escape]
S Lower shields
K Beam over
(Go right door)
Use freezer
Pick up virus (needs to be get G item cursor)
(Go topmost, west wall)
Use left shelf
Pick up antigrav unit
(Go right)
(Go south)
Pick up Wrench
Use Wrench on left panel
Pick up insulation
Use red panel
Use Wrench on N² tank
Use Antigrav unit on N² tank
(Go bottom)
Use insulation on machine (bottom)
(Go topmost, west wall)
Use Wrench on tank valves
Use polyberylcarbonate on synthesizer output panel
Use control panel
[Escape]
Pick up TLTDH gas
Use Wrench on tank valves
Use antigrav unit on O² tank
Use N² tank on empty space
Use Wrench on tank valves
Use control panel
Pick up Amonia
(Go right)
Use Amonia on left input
Use virus on right input
Use McCoy on right input
Pick up cure
(Go north)
Use Wrench on grid panel
Use TLTDH gas on open vent
(Go south)
(Go topmost, west wall)
Use cure on synthesizer output panel
Use control panel
Pick up Hypo
(Go right)
(Go down ladder)
Use tied people (left)
Use Hypo on Romulan (right)
Talk to Romulan
[Escape]
MISSION 4 "ANOTHER FINE MESS"
N Map --> "(4) Harlequin"
Win battle
[Escape]
N Map --> "(5) Harrapa"
S Lower shields
K Beam over
[Escape]
(Go north)
Use Spock on blue button
Use Spock on purple button
[Escape]
(Go leftmost door)
(Go north)
Use Spock on controls
[Escape]
(Go southwest)
Use Spock on sphere
Use tricoder on sphere
[Escape]
(Go north)
Use controls, option 1, 2
[Escape]
MISSION 5 "FEATHERED SERPENT"
N Map -->"(7) Digifall"
dialogue options 2,1
O Orbit planet
K Beam over
Talk to Quetzecoatl
[Escape]
Pick up rock from floor
Use rock on vine
Use rock on vine
Use vine
(Go left)
(Go left)
Use rock on warrior
Use rock on warrior
(Go left)
(Go left)
Use redshirt on path
(Go left)
(Go left)
[Escape]
At the trial, dialogue option 1,3
[Escape]
MISSION 6 "THAT OLD DEVIL MOON"
[Escape]
N Map --> "(12) Alpha Proxima"
O Orbit planet
K Beam over
Pick up rock
(Go forward)
Use panel, code = 10200
(Go forward)
Use panel, code = 122
(Go forward)
Use tricoder on door panel
(Go right - laser drill room)
Open box
Pick up wires
Use tricoder on controls
Use controls, "100"
Use rocks on impression
Use controls, "001"
(Go left)
Use card on panel
(Go forward)
Use wires on right computer
Use left computer
[Escape]
MISSION 7 "VENGEANCE"
[Escape]
(Go bottom)
(Go to Auxilary)
Pick up Saw
(Go bottom)
(Go to bridge)
Use Saw on support bar
(Go bottom)
(Go Sickbay)
(Go left)
Pick up Hypo
Pick up Saw
(Go right)
Pick up wire
Use support bar on rubble
Use red phaser on rubble
(Go forward)
(Go to Transporter room)
Pick up wire
(Go bottom)
(go to Engineering)
Use red phaser on rubble
Pick up Power unit
(Go left)
Use red panel on left
Pick up journals
Use Hypo on oil canister
(Go right)
(Go bottom)
(Go to Sickbay)
(Go bottom)
(Go to Auxiliary)
Use drill on panel
Use panel
Use Oil Hypo on panel
Use panel
(Go forward)
Use journals on right slot
(Go bottom)
(Go bottom)
(Go to Sickbay)
(Go forward)
(Go to Engineering)
(Go left)
Use wire on port
Use wire on port
Use junction box
(Go right)
(Go bottom)
(Go to Sickbay)
(Go bottom)
(Go to Auxiliary)
(Go forward)
Use tricoder on left space
Use McCoy on left space
Use left controls --> weapons
Use Spock on middle controls
(Go bottom)
(Go bottom)
(Go to Sickbay)
(Go forward)
(Go to Transporter room)
(Go left)
Use power unit on slot
Use monitor
Use controls
[Escape]
(Go right)
(Go bottom)
(Go to Sickbay)
(Go bottom)
(Go to Auxiliary)
(Go forward)
Use communicator, hail Elasi, dialogue option 2
Use left controls --> weapons
Use middle controls
[Escape]
Win battle
[Escape]
Here is the star map. If you select any other destinations, you will be off course, fighting enemies and most likely gameover.
