If you are uncomfortable tearing down the lappy, then stop. You can blow out the dust bunnies using canned air. Direct short bursts of air (don't use long bursts, overspinning the fan may damage it) into the intake baffles. That should be good enough to allow it to run cooler. Tearing the lappy down just allows you to be more thorough.
If the above fixes the heating problem, then we still face the display problem. Here is a quote from previous posts of mine about screen problems;
"So you'll know what we're looking at, there are 3 or 4 things that could be at fault;
1. The screen itself. They are usually around $70-$100 in price.
2. The inverter. A small part, not very expensive usually, but it's usually not the failed part. But it's in the signal path and must be considered.
3. The wiring harness. If it's crimped, bent or partially broken, it can cause odd problems.
4. The mainboard. Usually quite expensive, and very challenging to replace if you've never done it before.
A PC shop would charge $250-$400 to troubleshoot and repair this. You can do it cheaper, but it won't be fast. You'll be ordering one-part-at-a-time, changing it in the lappy, then seeing if it's fixed. If it turns out to be the mainboard, then you've ordered those other parts for nought.
So, your options are,
A. Fix it yourself. Cheaper in the long run and you'll get a wealth of experience tearing down a lappy, but it won't be fast.
B. Let a PC shop fix it, at the above mentioned estimate.
C. Apply any monies mentioned toward a new lappy, instead of trying to fix the old one."
To be honest, you face a daunting task since you are uncomfortable with working in a lappy. I recommend option C mentioned in the quote. I also recommend spending the money on an extended warranty (3 years worth) if the manufacturer offers them. Toshiba used to offer very good extended warranties.
DISCLAIMER: In a previous life as a PC repair tech (6 yrs. ago) I was a certified Toshiba Laptop repair tech. I DID NOT work directly for Toshiba, however, and own no stock or have any other interest in the monetary success of said company.
Hope this helps.