Help a newbie out! Willing to give 200%

okay so before you guys bash me (which is what I need) let me explain a few things...
I'm a full-time college student and I work a full-time job in the evenings.  My gym is only open 24 hours Monday to Thursday, and I go to the gym at midnight when I get off of work.  So now that you know I can only go to the gym Mon-Thurs, the 3 day Full Body workout is not an option because I don't have the 48 hours of rest in between.  I know, I have a sucky schedulle but I still want to get into shape.  I'm 5'9" at 155 lbs, thin athletic build.  I have been doing pushups, situps, dips, and pull ups for a few months now and I'm ready to start lifting.  My diet is not a problem, I started eating about 3000-3500 calories a day and about 150-200 grams of protein a day.  My first goal is to reach 165lbs, strong and ripped (10lb muscle gain).  I understand this takes dedication and I'm absolutley ready for it.
I just don't know how to incorporate a full body routine in 4 days in a row, is it possible?  Considering I'm new to this I would like to focus strictly on COMPOUND excersises, since I hear they see the most gains with beginners.  To give you an idea of my strength I can do about 15 dips in a row and 10 wide grip pull ups in a row.  Okay...
Monday-Chest/Tri's
Tuesday-Bi's/Back
Wednesday-Shoulders
Thursday-Legs/Abs
Friday-OFF
Saturday-OFF
Sunday-OFF
Keep in mind I have an iron gym at my house so on my off days when I can't make it to the gym I can do dips, pullups, pushups, etc...if that's even good to do on the off days.  I would like to hit my upper body again later in the week, I am going to try to play with my schedulle a little now that's schools ending.  But lets just focus on the Monday to Thursday right now.  Please give me some ideas on excersises/sets/reps.  This newbie greatly appreciates your help. 

Try...

Monday- Chest/Shoulders
Tuesday- Bi's, Tri's, and Forearms
Wednesday- Back/Legs
 
Keep repeating that over it seems to be working for me and I have converted some of my friends to this routine.  But do your abs everyday dont just do them once a week.  Also do abs at the gym and also do some sit-ups and push-ups everynight before bed...

What kind of gym is only open Mon-Thurs?   Step 1:  Find a new gym.

The gym is open 24 hours those days...and open until 10pm throughout the weekend.  I tried to make that clear enough to understand.  I work until midnight, so I wouldn't be able to go the days its open until 10.

Oh, I misunderstood.  You're not going to be able to train optimally with only 4 consecutive days per week no matter how you look at it.  Have you considered going in the morning before class/work?

What about 2 fullbody workouts with the good accessory exercises added in the end which land on monday and then workout at thursday. The rest days are kept to a minimum.

After first workout rest 2 days then on Thursday another workout then you have 3 days rest until you do it again.

Being able to hit it hard with those 2 days and having that little extra rest time could benefit you considering you probably work a lot and have school in mind.

This is meaning doing a fullbody workout on those 2 days like something like this...

Increase 5Lbs every workout if you can with good form

Monday-
Squats - 3x5
Flat Benchpress 3x5
Deadlift 1x5
Chinups 2 sets  to failure
*input favorite isolation excerise- like calf or tricep* 2x8-12
ab exercise

then

Thursday
Squat 3x5
Standing OH Press 3x5
PowerCleans 5x3  or  Rows 3x5    *if you can't do PowerCleans*
*Chest* Dips 2 sets to failure
Pullups 2 sets to failure
*input favorite different isolation exercise from monday- like barbell curls* 2x8-12
different ab exercise

With the extra rest days this might be ok... reps and sets is up to you just stick with one and increase the weight every workout when you can and when you mostly can't switch sets and reps to something else and start over again.

"When your strength gains plateau, if you been training exclusively for limit strength/power, you'll need usable muscle mass to progress further."

As far as reps go: 1-5 reps = Strenght
                             6-10 reps = Muscle Mass
                             +10 reps = "Muscle Endurance"
Using your iron gym on off days would be fine IMO. Take a multivitamin and some omega 3 fish oil tablets, they are both pretty cheap and keep ya healthy. For some exercises you could do on your off days, go on youtube and search fitnessvip. Some of his videos will help, with pushup variations, burpees, and his cardio suggestions.

Bench: 70 Squat 135 Deadlift: 1??s 
Supps: Creatine, Multi, Fish Oils 

Jones's Log

i like felonyr's idea.  Or you could do something such as :

Monday: chest/tri day
Tuesday: legs/abs
Wednesday or thursday: Back/bi day

or

Monday Chest/bi
Tuesday: legs/abs
Thursday: Back/tri

there are alot of different things you could do

Monday : chest + delts + tri

Thursday : Squat + DL + Back + Bi

Do heavy volume high intensity. That should give you enough tissue damage to recover on your Off days.
I did 5 day splits and 3 day full body routines. But this 2 day split is what works for me best since my schedule is erratic and diet sucks though it is clean.

Try doing Cardio on Off days? Your call. But some cardio is gonna be a healthy for your heart.

Anbe Sivam. Period.

I think you could do a full body workout 3 days a week if you have an iron gym at home. This is basic and can easily be altered I tried to do major compound exercises because thats what you said you were striving for. Monday and weds lift heavy 6 to 8 reps. Friday do the exercises 10 to 12 reps. Just be sure to look into getting sleep cuz it sounds like you have a full plate.

Monday(at gym)
squat
bench press
overhead press
crunches

weds(at gym)
squat or deadlift or powerclean
Dumbell press
rows or shrugs(maybe both)

Friday(at home iron gym)
100 to 150 push-ups(for time and try 50 regular,50 elevated,50 tri-push-ups)
Pull-ups(put a back-pack on with weights or rocks on)
Single leg body squats(hold something heavy as you do them)