On-Premises data gateway - the remote certificate is invalid according to the validation procedure

I ran the On-Premises data gateway, and when I entered my email address for the PowerBI account I've been using, I got the following;

A SSLv3-compatible ClientHello handshake was found. Fiddler extracted the parameters below.

Version: 3.1 (TLS/1.0)

Random: 58 C9 20 55 4F F0 6E 6F B3 53 FD 1E E5 AA 79 8D 57 E3 EE A1 53 AC 4A 2E 7F 20 C1 C6 22 B1 DC 85

"Time": 05/04/2015 06:34:16

SessionID: empty

Extensions:

renegotiation_info 00

server_name api.powerbi.com

elliptic_curves secp256r1 [0x17], secp384r1 [0x18]

ec_point_formats uncompressed [0x0]

SessionTicket empty

Ciphers:

[C014] TLS1_CK_ECDHE_RSA_WITH_AES_256_CBC_SHA

[C013] TLS1_CK_ECDHE_RSA_WITH_AES_128_CBC_SHA

[0035] TLS_RSA_AES_256_SHA

[002F] TLS_RSA_AES_128_SHA

[C00A] TLS1_CK_ECDHE_ECDSA_WITH_AES_256_CBC_SHA

[C009] TLS1_CK_ECDHE_ECDSA_WITH_AES_128_CBC_SHA

[0038] TLS_DHE_DSS_WITH_AES_256_SHA

[0032] TLS_DHE_DSS_WITH_AES_128_SHA

[000A] SSL_RSA_WITH_3DES_EDE_SHA

[0013] SSL_DHE_DSS_WITH_3DES_EDE_SHA

[0005] SSL_RSA_WITH_RC4_128_SHA

[0004] SSL_RSA_WITH_RC4_128_MD5

Compression:

[00] NO_COMPRESSION

I've browsed to https://api.powerbi.com/ in IE, and as expected, I received the error 'There is a problem with this website's security certificate'.

I proceeded to 'trust' the certificate in IE.  I clicked 'Sign in' again on the On-Premises data gateway, and was presented with subsequent error messages;

Ensure network access is functioning correctly.  Firewall and proxy configurations may need to be changed.

and

Gateway service health check failed.  Common issues can be found at https://go.microsoft.com/fwlink/?linkid=838272

Below is the stack trace:

Health check failed becuase it cannot finish in 2000ms.