How should I make the php script for a contact form from multiple select dependencies

I assume that you do have jquery to display the relevant select boxes upon selection of devices etc... I have made a few changes in your html form, like adding id="form" in your form tag. Also added value="" for options like "Please select Service".. Here is the code. Hope this helps.. Refer to this as well.. Jquery form submit to check empty fields

<form id="form"  action="sending.php" method="POST" enctype="multipart/form-data"> 
<input type="hidden" name="action" value="submit"> 
Name:<br> 
<input name="name" type="text" value="" size="30"/><br> 
Email:<br> 
<input name="email" type="text" value="" size="30"/><br> 
Service:<br> 
<select name="service" id="service" class="service">
    <option value="">Select a Service</option>  
    <option value="screen" data-target="devices" id="screen">Screen Replacement</option>       
    <option value="comp" data-target="comp" id="comp">Computer Work</option> 
    <option value="misc" data-target="misc" id="misc">Miscellaneous</option>
</select>
<div style="display:none" id="service-devices">
    <select name="devices" id="devices" class="devices">
        <option value="">Select a Device</option>      
        <option value="iphone" data-target="iphones" id="iphone">iPhone</option>       
        <option value="ipad"  data-target="ipads" id="ipad">iPad</option>
        <!--<option value="watch" id="watch">Apple Watch</option> -->
        <option value="android" id="android">Android</option>
    </select>
    <div style="display:none" id="devices-iphones">
        <select name="iphone" id="iphone" class="iphone">
            <!--<option value="iphone6s" id="iphone6s">iPhone 6S</option> -->
            <!--<option value="iphone6splus" id="iphone6splus">iPhone 6S Plus</option>-->
                            <option value="">Select a Model</option>
            <option value="iphone6" id="iphone6">iPhone 6</option>
            <option value="iphone6plus" id="iphone6plus">iPhone 6 Plus</option>
            <option value="iphone5s" id="iphone5s">iPhone 5S</option>
            <option value="iphone5c" id="iphone5c">iPhone 5C</option>
            <option value="iphone5" id="iphone5">iPhone 5</option>
            <option value="iphone4s" id="iphone4s">iPhone 4S</option>
            <option value="iphone4" id="iphone4">iPhone 4</option>
        </select>
    </div>
    <div style="display:none" id="devices-ipads">
        <select name="ipad" id="ipad" class="ipad">
                        <option value="">Select a Model</option>
            <option value="ipadmini3" id="ipadmini3">iPad Mini 3</option>
            <option value="ipadmini2" id="ipadmini2">iPad Mini 2</option>
            <option value="ipadair" id="ipadair">iPad Air</option>
            <option value="ipad4" id="ipad4">iPad 4</option>
            <option value="ipad3" id="ipad3">iPad 3</option>
            <option value="ipadmini" id="ipadmini">iPad Mini</option>
            <option value="ipad2" id="ipad2">iPad 2</option>
        </select>
    </div>
</div>
<div style="display:none" id="service-comp">
    <select name="compwork" id="compwork" class="compwork">
        <option value="desktopcreation" id="desktopcreation">Desktop Creation</option>
        <option value="desktopbuild" id="desktopbuild">Desktop Build</option>
        <option value="hardwareupgrades" id="hardwareupgrades">Hardware Upgrades</option>
        <option value="datarecovery" id="datarecovery">Data Recovery/Transfer</option>
        <option value="spywareremoval" id="spywareremoval">Spyware/Adware Removal</option>
        <option value="virusremoval" id="virusremoval">Virus Removal</option>
    </select>
</div>
<div style="display:none" id="service-misc">
    <select name="miscellaneous" id="miscellaneous" class="miscellaneous">   
    <option value="networksecurity" id="networksecurity">Network Security</option> 
    <!--<option value="webdesign" id="webdesign">Website Design</option>-->
    </select>
</div><br>
Message:<br> 
<textarea name="message" rows="7" cols="30"></textarea><br> 
<input type="submit" value="Submit Request"/> 

    <script src="js/jquery-1.10.2.min.js"></script>
    <script>
    $(document).ready(function() {
    $('select').change(function(){
     var boxid = $(this).children('option:selected').attr('data-target');
     alert(boxid);
     if(boxid == "devices") {
       var divId = "service-" + boxid;   
     }
     document.getElementById(divId).style.display = "block";

    });

    $("form").submit(function(){
       // $(':input[value=""]').attr('disabled', true);

        $("input[type='text'],select,input[type='password'],textarea",this).each(function() {
            if($(this).val().trim() == "") {
               $(this).attr('disabled', true);
            }
        })


    });


    });    
    </script>