LGPL is "weaker" than the GPL, but not in the way you describe. The difference has nothing to do with whether or not you modified the LGPL'd library.
Here's a very rough high-level description that should help get your intuition on the right track: The GPL requires that if your program uses any GPL'd code, your entire program must be free (as defined by the "four freedoms" the FSF describes here). The LGPL requires that if you use any LGPL'd code, that LGPL'd code must be free even if the rest of your program is not. In particular, that means all users of your program must be able to modify the LGPL'd library within your program however they like, even if they are not able to modify the rest of your program.
If you want the rest of your program to remain closed source, then in practice the simplest way of complying with the LGPL is usually to link your program to the LGPL'd library dynamically rather than statically, since the end user can easily swap one .dll file for another without recompiling or even relinking your code. Another less common option is to provide all of the object files that were statically linked into your program, but not their source code, so the end user can redo the linking if they want to change the LGPL'd library. For more information, I highly recommend browsing the FSF's official FAQ page on GNU licenses.
Regarding transitive dependencies, the short version is that if this worries you, you need a proper lawyer to check this stuff. If one of your dependencies has a GPL dependency you didn't know about, you're still violating the GPL just as much as anyone else is, so this can be a serious problem.
