SQL Server (2012 Enterprise) Browser service failing

I have a problem as described below:

I have an instance of SQL Server 2012 Enterprise (thanks to MSDN) for local development on my PC.

I try to start SQL server Browser Service from SQL Server Configuration Manager and it takes a long time to fail, then fails with:

The request failed or the service did not respond in a timely fashion. Consult the event log or other applicable error logs for details.

I checked event logs and found these errors in this order (all within the same 1-second time frame):

The SQL Server Browser service port is unavailable for listening, or invalid.

The SQL Server Browser service was unable to establish SQL instance and connectivity discovery.

The SQL Server Browser is enabling SQL instance and connectivity discovery support.

The SQL Server Browser service was unable to establish Analysis Services discovery.

The SQL Server Browser service has started.

The SQL Server Browser service has shutdown.

I checked firewall rules and both port 1433 (TCP) and 1434 (UDP) are wide open, just as well - the programs and service binary had been "allowed through windows firewall". I started the "Analysis Services" service by hand and it works fine. Browser still won't start.

Some History: Installed SQL 2008 R2 express advanced

Installed SQL2012 Express advanced

Uninstalled SQL 2008 R2 express advanced

Installed 2012 SSDT and lots of features with Express install

Installed a unique instance of SQL 2012 Enterprise with all features

Uninstalled SSDT and reinstalled SSDT with Enterprise (solved a different problem)

Uninstalled SQL 2012 Express

Uninstalled SQL 2012 Enterprise

Removed anything with "SQL" in the name from Control panel > "Programs and features"

Installed SQL 2012 Enterprise without Analysis services (This is where I noticed SQL Browser service was failing to start even on the install)

Added the feature of Analysis Services (and everything else) via the installer (Browser continued to fail to start on the install)

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Other interesting facts: opening a command window with administrator and trying to run sqlbrowser.exe manually yielded:

Microsoft Windows [Version 6.1.7601] Copyright (c) 2009 Microsoft Corporation. All rights reserved.

C:\Windows\system32>cd C:\Program Files (x86)\Microsoft SQL Server\90\Shared

C:\Program Files (x86)\Microsoft SQL Server\90\Shared>sqlbrowser.exe -c SQLBrowser: starting up in console mode SQLBrowser: starting up SSRP redirection service
SQLBrowser: failed starting SSRP redirection services -- shutting down.
SQLBrowser: starting up OLAP redirection service
SQLBrowser: Stopping the OLAP redirector

C:\Program Files (x86)\Microsoft SQL Server\90\Shared>

As I try to repair the install it errors out saying

The following error has occurred:

Service 'SQLBrowser' start request failed.

Click 'Retry' to retry the failed action, or click 'Cancel' to cancel this action and continue setup.

For help, click: http://go.microsoft.com/fwlink?LinkID=20476&ProdName=Microsoft%20SQL%20Server&EvtSrc=setup.rll&EvtID=50000&ProdVer=11.0.2100.60&EvtType=0x4F9BEA51%25400xD3BEBD98%25401211%25401

Clicking retry fails every time. When clicking cancel I get:

The following error has occurred:

SQL Server Browser configuration for feature 'SQL_Browser_Redist_SqlBrowser_Cpu32' was cancelled by user after a previous installation failure. The last attempted step: Starting the SQL Server Browser service 'SQLBrowser', and waiting for up to '900' seconds for the process to complete. .

For help, click: http://go.microsoft.com/fwlink?LinkID=20476&ProdName=Microsoft%20SQL%20Server&EvtSrc=setup.rll&EvtID=50000&ProdVer=11.0.2100.60&EvtType=0x4F9BEA51%25400xD3BEBD98%25401211%25401

When I go to uninstall the SQL Browser from "Programs and Features", it complains:

Error opening installation log file. Verify that the specified log file location exists and is writable.

Is there any way I can fix this short of re-imaging my computer and reinstalling from scratch? A possible approach would be to somehow really uninstall everything and delete all files related to SQL... is that a good idea, and how do I do that?