The Sims 1 does run on Win7 .
I don't have it installed at the moment, and no longer have the disk, but it did install and run on
Win7 64bit. I don't recall using Compatibility settings, but if I were to install with any compatibility settings I would be inclined to use XP sp2.
There is a Windows security Update - KB 2670838 - that can stop games from loading as you
describe if you are off line at the time (the update causes Windows to check for an update to the game).
This update is required if you use IE 10 , but you can un-install it if you don't use IE 10.
It may be the game may not run on laptops that use integrated graphics, as it may not recognise
the Integrated graphics chip as a viable graphics card (having no dedicated VRAM is sometimes a problem).
If Integrated graphics is not the problem and you have been installing to the default location
- Program Files (x86) - try using a 'custom' install location.
A separate partition or Hard Drive are best, but you could also make a new folder to install games
to in the C:\ drive/partition.
This method more commonly helps with permissions issues, but can be useful with other problems
( DOOM3 crashed my machine when trying to install to the default location) on occasion.
.