Here is the Space Quest IV solution that will give you full points at the end. The points that you should have at each step are given in [] after each piece of point-scoring action. Generally, north is up, south is down, west is left and east is right.
I've split it up into sections that you can jump to if you want to:
Make your way to the right and pick up the rope that is near the bottom of the screen to the right [5]. Then make your way back left to the screen you started on and left again, where you will see a wrecked hover-car. Look inside it and open the glovebox. Take out the PocketPal laptop [10]. Close the glove-box again if you have a sense of neatness, otherwise don't worry about it. Make your way up the screen to the middle left screen. Look in the hole in the tank and take the unstable ordinance [35]. Use your better judgement and put it back [15].
Make your way up again, into the upper left corner. Hide behind the bank's pillars and lay the rope out on the ground. Wait for the cute little pink bunny to come hopping along. When it hops into your noose, pull on the rope [25]. Take the power cell out of the bunny [28] and put it into the laptop [31]. Next make your way across to the upper right area, hide under the overhanging roof and wait for a while. After quite a while a robot will come, it won't be able to see you and will leave [36].
Then make your way down to the middle right screen. Open the topmost grating and hop in [41]. Take the bottle into custody [46] and press the button that's under the blotter on the table [56]. Listen to the message, then open the sewer hatch and enter the sewer. The easiest way to the other side is just up a bit, then left all the way to the other side then down to the ladder. Some green slime will come out of a grating and follow you. Scoop some of the slime up in the bottle [61] and then leave and climb up the ladder before the slime decides to scoop _you_ up.
When you open the hatch into the street, you'll see a Sequel Police patrol ship land. When the Sequel Police have left the ship, get out of the manhole [64] and make you way to the ship. Get in the undercarriage hatch [69]. You'll get taken up to the headquarters. Go to the left, you will see a time pod appear. When the Sequel Policeman has left the pod, make a run for it and jump in [79]. Answer the copy protection question. Now you will be faced with a row of symbols on a screen; write these down. Now you'll have to enter other symbols to get elsewhere. Try a row of the bottom right characters (looks like a '?'). If that does not work, try the reverse of the code that was on the screen when you got into the pod. One of those should land you in Space Quest X.
Then get out of the hole in the bottom left of the nest, you'll fall into some
water and get captured by some women. Zondra, who we assume Roger meets
somewhere between Space Quest IV and Space Quest X is ever so slightly peeved
and drags you off to their fortress.
You'll be tied to a chair and Zondra will leave you at the mercy of Thoreen and
her EpiRip 357. A giant sea slug will appear and scare the women off. When the
slug reaches for you with its tentacles, it will accidentally open your
restraints, allowing you to press the little red button near your right hand
[89]. This will zap the slug's tentacles with the same things that took your
pants legs off. Take this opportunity to grab an oxygen cylinder [94] which you
throw into the slug's mouth when he grabs you again [99]. The girls are ever so
happy, Roger is forgiven his misdemeanors, and they decide to go off to the
Galaxy Galleria to shop and celebrate.
Go to Sacks and buy some women's clothing, it will cost you B$60 [119]. Then go
to the ATM near the Software shop and clean house [129]. Go into the Software
shop and buy the Space Quest IV Hint Book [134]. Go and retrieve your clothes
from the changing booth at Sacks [137].
Make your way to the Arcade. Have a game of Ms Astro Chicken if you want to. (No
points attached though, unfortunately.) If you have done everything in the
Galleria that you're supposed to have, the a Sequel Police time pod will appear.
It's best to be standing on the right hand side of the arcade when this happens.
Get out of the Arcade and go to the Skate-O-Rama. Get up into the top half of it
and wait for the Sequel Police to arrive, then go back down into the bottom
half, get back to the arcade and get into the time pod [152]. Write down the
code that is currently on the screen. Put together the pieces of the codes from
the gum wrapper and the hint book (the bit from the hint book coming first) and
type it in [157]. Space Quest X
You can do quite a bit of wandering here, but there is only one sequence that
is essential. Go left first, and then to the left-most side of that screen. You
should see the shadow of a large bird-like creature pass. Then make your way
back right to where your time pod is and go down the slope that looks rather
step-like. You'll get grabbed by the big bird and taken off to its nest. After
a short while a Sequal Policeman will be dropped into the nest too, having a
rather less comfortable landing than yours was. Search him and get the gum
wrapper [84], which you should look at more closely. The Galaxy Galeria
The girls all run off, leaving Roger alone at the entrance. One of them drops
her ATM card, which you pick up [101]. There are a number of shops arranged in
a circle around the central Skate-O-Rama. Clockwise, the shops are: Sacks,
Arcade, Big and Tall, Monolith Burger, Radio Shock, Software. First go to Big
and Tall and get some new clothes which will cost you B$20 [106]. Next, go to
Monolith Burger and work for some money [109]. (You must actually do the arcade
bit, otherwise you lose 3 points instead of gaining them. If you go back to
Monolith to work again, you will lose 3 points again if you don't want to do
the arcade bit.) You must have more than B$60, preferably about 70. When you
get fired, go back to the entrance of the Galleria and pick up the boss's cigar
butt that he threw at you [114].