Don't replace things just because someone says to replace them. These things can be tested to see if they are getting electricity and/or working.

Also you can replace something with a wrong part or not correctly install it, then you have two problems.

Because your money is tight, I would recommend getting a multimeter and learning how to use it. Watch automotive videos on youtube where they show you how to use a multimeter for testing this or that. Search for the words multimeter mercedes or multimeter automotive.

Next get or borrow a 10 amp automotive battery charger. A fully charged battery is 12.75 volts DC. Learn to keep the battery charged and periodically check its charge as you work on the vehicle. I keep a charger connected if doing a lot of electrical testing/work without the engine running. NOTHING will work properly with a low battery!

Check the fuses.

(ALWAY check the battery and fuses FIRST if having an electrical problem!!! No electricity - no workie!)

Find out if the alarm is factory or an aftermarket add-on. In either case, learn if the alarm disables starting on the vehicle. And if you need the FOB to disarm it. If factory, you can get a FOB from a Mercedes dealer. (If aftermarket, then from the manufacturer of the alarm perhaps?) Or you can get a wiring diagram and disconnect the alarm and particularly the disabling function so it will start (if that turns out to be the problem by TESTING with a multimeter and schematic wiring diagrams).

This is the way I fix cars. If you don't know this stuff, then find an automotive electric shop or alarm shop. This is pretty much advanced electrical troubleshooting. Just tracking down the wiring diagrams for an aftermarket alarm can be challenging.

Mercedes wiring diagrams can be found with a google search.