Are there words that are spelled the same but pronounced differently depending on whether the initial letter is capital or lowercase?

There are more than two actually.

Here's a list of twelve heteronym pairs in which one word is capitalized (typically, a proper noun), and the other is not:

• August /ˈɔːgəst/ (proper noun) and august /ɔːˈgʌst/ (adjective)

• Begin /(the Israeli politician) and begin /bɪˈɡɪn/ (to start)

• Degas /deɪɡɑː/ and degas /diːˈɡæs/

• Job /dʒoʊb/ (the Biblical figure) and job /dʒɒb/ (an occupation)

• Natal /nəˈtɑːl, -ˈtæl/ (the Brazilian city) and natal /ˈneɪtəl/

• Nice /niːs/ (the city in France) and nice /naɪs/ (kind, friendly)

• Noel /ˈnoʊəl/ (name) and noel /noʊˈɛl/ (a Christmas carol)

• Polish /ˈpoʊlɪʃ/ (the nationality) and polish /ˈpɒlɪʃ/ (making things shiny)

• Rainier /rəˈnɪər, reɪˈnɪər/ (the name, or mountain) and rainier /ˈreɪniər/ (more rainy)

• Reading /ˈrɛdɪŋ/ (the place name) and reading /ˈriːdɪŋ/ (the activity involving books)

• SEAT /ˈsɛ.æt/ (the Spanish automaker) and seat /siːt/

• Tangier /tænˈdʒɪər/ (in Morocco) and tangier /ˈtæŋiər/ (more tangy)

– words taken from Richard Stevens's List of Heteronyms

Scone/scone and Lima/lima can be added to the list.

Capitonym

A capitonym is a word that changes its meaning (and sometimes pronunciation) when it is capitalized; the capitalization usually applies due to one form being a proper noun or eponym.1 It is a portmanteau of the word capital with the suffix -onym. A capitonym is a form of homograph and – when the two forms are pronounced differently – also of heteronym.

The following words are also pronounced differently.

Bologna: A city in Italy    bologna: a processed meat 
Ares: god of war            ares: plural of are, a metric unit of area
August: the eighth          august: majestic or venerable
        month of the year   

A heteronym (also known as a heterophone) is a word that is written identically but has a different pronunciation and meaning. In other words, they are homographs that are not homophones. Thus, row (propel with oars) and row (argument) are heteronyms, but mean (intend) and mean (average) are not (since they are pronounced the same). Heteronym pronunciation may vary in vowel realisation, in stress pattern (see also Initial-stress-derived noun), or in other ways:

A few examples taken from the Wikipedia page:

1. They were too close to the door to close it.
2. Don't desert me here in the desert!
3. When shot at, the dove dove into the bushes.
4. We must polish the Polish furniture.
5. Upon seeing the tear in the painting I shed a tear.

The term English is similar to Polish in that it too can be spelled with or without a capital letter, but it is not a heteronym because its pronunciation remains identical. When a word differs in meaning, but its pronunciation doesn't change, it is called a homophone

• The English billiard player put more english on the ball

English
5. also english
a. The spin given to a propelled ball by striking it on one side or releasing it with a sharp twist.
b. Bodily movement in an effort to influence the movement of a propelled object; body English.

Anther example is Pole (a Polish person) pole (another name for rod) and the verb to pole

• The Pole used a pole in order to pole upstream.

Yes, such a word is called a "homograph." Aside from "Polish" and "polish," another exemplar homograph is "wind" (blowing air) and "wind" (what you do to watch).

If you are looking for another word where the initial capital letter is the all-important factor, then consider:

Moped (motorized bicycle by Honda)

and

moped (preterit tense of the verb "to mope")

Before it became a common noun, the proper noun "Moped" was a portmanteau formed by Honda to market its motorized bicycle.

Any such initial capital letter difference is going to have to involve a word that is considered proper like this, like Polish.

There is no generalized rule in English about capital letters changing pronunciation. What you have observed are incidental cases where a capital letter allows you to distinguish between a proper noun (or derivative) and another word with a different meaning and/or pronunciation (and typically origin) that happens to have the same spelling.